Competitive interactions co-occurrence modelling

Packages

Code
# Data manipulation package
library(tidyverse) # Easily Install and Load the 'Tidyverse'
library(psych) # Procedures for Psychological, Psychometric, and Personality Research

# Modelling packages
library(nlme) # Linear and Nonlinear Mixed Effects Models
library(betareg) # Beta Regression
library(glmmTMB) # Generalized Linear Mixed Models using Template Model Builder
library(AICcmodavg) # Model Selection and Multimodel Inference Based on (Q)AIC(c)
library(MuMIn) # Multi-Model Inference

#Modelling utility packages
library(broom) # Convert Statistical Objects into Tidy Tibbles
library(broom.mixed) # Tidying Methods for Mixed Models
library(insight) # Easy Access to Model Information for Various Model Objects
library(modelbased) # Estimation of Model-Based Predictions, Contrasts and Means
library(parameters) # Processing of Model Parameters
library(performance) # Assessment of Regression Models Performance
library(DHARMa) # Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models
library(ggeffects) # Create Tidy Data Frames of Marginal Effects for 'ggplot' from Model Outputs

# Grapich packages
library(GGally) # Extension to 'ggplot2'
library(patchwork) # The Composer of Plots


# Table output packages
library(kableExtra) # Construct Complex Table with 'kable' and Pipe Syntax
library(DT)


library(showtext)
font_add_google("Roboto", "Roboto")
showtext_auto()
showtext_opts(dpi = 300)

Variables description

Table 1: List of variables used to modelling spatial co-occurrence patterns of competitive interactions
Variable Description Units Source
SIF Spatial species interaction factor. SIF<1: segregation, SIF=1: independence, SIF>1= aggregation index Each study
Ov_coeff Temporal overlap coefficient. Ov_coeff =1: complete activity overlap, Ov_Coeff =0: No activity overlap index Each study
CBMratio Competitors body mass ratio: ln( dominant competitor body mass/ subordinate competitor body mass) index COMBINE data base (Soria et al. 2021)
Diet_dist Dominant and subordinate competitor category diets: Same if pair of competitors shares de diet category, different if not category PHYLACINE trait data base (Faurby et al. 2020)
Phy_dist Pairwise mitochondrial DNA phylogenetic distances mitochondrial DNA phylogenetic distances Hassanin et al. (2021)
Abs_lat Absolute latitude of each study when reported coordinates Each study
Avg_dist Average distance (km) between camera trap stations reported. Only used for spatial co-occurrence models Average liner distance in km Each study
Samp_dur duration of sampling in months. Only used for temporal co-occurrence models Months Each study
Locality Each sampling location where species co-occurrence information was obtained, within each study category Each study
Label Each study unique ID category Each study

Data

The data correspond to studies evaluating the spatial and temporal co-occurrence of mammals of the order Carnivora. In all cases the species are of the same order and present ecological interactions of competition.

Spatial co-occurrence data of carnivorous mammals were measured using the species interaction factor (SIF). This is a parameter derived from multi-species occupancy models (Waddle et al. 2010; Richmond, Hines, and Beissinger 2010).

Code
# Load the spatial co-ocurrence data base of competitive interactions
spatC_db <- read_delim("Data/Model data/spatC_db.csv", delim = ";" )[,-1] %>%
  # Select the variables
  select(SIF, D_competitor, D_family, S_competitor, S_family, mass_ratio, diet_dist, Lat, Lat_abs, p_distance, Avg_dist, Locality, Label)
DT::datatable(spatC_db)

The Table 2 contain the general description of the numeric variables of spatial data base. The table was constructed with psych package (Revelle 2022)

Code
Spatnum_summary <- spatC_db %>% 
  select_if(is.numeric) %>% 
  describe(. ,fast = T) 

kbl(Spatnum_summary, caption = "General description of the spatial co-occurrence data base for competitive interactions", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Table 2: General description of the spatial co-occurrence data base for competitive interactions.
vars n mean sd min max range se
SIF 1 216 1.028 0.843 -6.195 5.610 11.805 0.057
mass_ratio 2 211 1.260 1.012 0.027 4.817 4.790 0.070
Lat 3 216 12.484 30.095 -41.234 58.513 99.747 2.048
Lat_abs 4 216 30.170 12.158 0.553 58.513 57.960 0.827
p_distance 5 166 0.145 0.045 0.037 0.200 0.163 0.003
Avg_dist 6 191 1.699 1.418 0.250 10.600 10.350 0.103

We use the GGAlly package to explore the visual relationship between numerical variables (Schloerke et al. 2021). We used pearson’s correlation coefficient

Code
(Spat_cor <- select_if(spatC_db, is.numeric) %>% # select numeric variables
  ggpairs(.,
          # Correlation coefficient upper part
        upper = list(continuous= wrap("cor", method= "pearson", 
                                      digits=2, corSize= 80)),
        lower = list( continuous= "smooth")) +
  theme_bw()+
    theme(text=element_text(family = "Roboto")))

Figure 1: Spatial competitive co-occurrence corplot

The temporal data corresponds to the co-occurrence of Carnivora mammals measured by overlap coefficient of kernel activity curves (Ridout and Linkie 2009).

Code
tempC_db <- read_delim("Data/Model data/tempC_db.csv", delim = ";")[,-1] %>%
  select(Ov_coeff, D_competitor, D_family, S_competitor, S_family, mass_ratio, diet_dist, Lat, Lat_abs, p_distance, Samp_dur, Locality, Label)
  
DT::datatable(tempC_db )

The Table 3 contain the general description of the numeric variables of spatial data base.

Code
Tempnum_summary <- tempC_db %>% 
  select_if(is.numeric) %>% 
  describe(. ,fast = T) 

kbl(Tempnum_summary, caption = "General description of the temporal co-occurrence data base for competitive interactions", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Table 3: General description of the temporal co-occurrence data base for competitive interactions.
vars n mean sd min max range se
Ov_coeff 1 1274 0.636 0.215 0.060 0.970 0.910 0.006
mass_ratio 2 1267 1.408 1.026 0.000 5.678 5.678 0.029
Lat 3 1274 12.429 25.640 -41.234 58.539 99.773 0.718
Lat_abs 4 1274 24.814 13.992 0.553 58.539 57.986 0.392
p_distance 5 915 0.149 0.044 0.037 0.212 0.175 0.001
Samp_dur 6 1015 19.102 29.089 0.780 146.000 145.220 0.913

We use the GGAlly package to explore the visual relationship between numerical variables (Schloerke et al. 2021). We used pearson’s correlation coefficient

Code
(Temp_cor <- select_if(tempC_db, is.numeric) %>% 
  ggpairs(.,
        upper = list(continuous= wrap("cor", method= "pearson", 
                                      digits=2, corSize= 80)),
        lower = list( continuous= "smooth")) +
  theme_bw()+
  theme(text=element_text(family = "Roboto")))

Figure 2: Temporal competitive co-occurrence corplot

Modelling procedure

Standardize numeric covariates

The numerical covariates were standardized to mean 0 and standard deviation 1, which facilitates model fitting and direct comparison of regression coefficients. In addition, pairs of species that do not contain information on any of the variables (cells with NAs) were eliminated.

Because we aimed to evaluate whether the patterns found varied depending on the dominant competitor family, we made subsets of the databases. For spatial co-occurrence we only subset the felidae family. For temporal co-occurrence we subset the families Felidae, Canidae and Mustelidae.

Code
# Function to standardized the numeric variables
scale_this <- function(data){scale(data) %>% as.vector() }

# Select the variables for Spatial and temporal data sets
SC_vars <- c("mass_ratio", "Lat_abs", "p_distance", "Avg_dist")
TC_vars <- c("mass_ratio", "Lat_abs", "p_distance", "Samp_dur")

# All data Spatial
spatC_modsdf <- spatC_db %>%
  drop_na() %>% 
  mutate(across(all_of(SC_vars), scale_this)) 
dim(spatC_modsdf)
[1] 149  13
Code
#Subset for spatial data
# Felidae Spatial
spatC_modsdf_F <- spatC_modsdf %>% 
  filter(D_family == "Felidae")
dim(spatC_modsdf_F)
[1] 85 13
Code
# All data Temporal
tempC_modsdf <- tempC_db %>%
  drop_na() %>% 
  mutate(across(all_of(TC_vars), scale_this))
dim(tempC_modsdf)
[1] 726  13
Code
#subset for temporal data
# Felidae Temporal
tempC_modsdf_F <- tempC_modsdf %>%
   filter(D_family == "Felidae")
dim(tempC_modsdf_F)
[1] 376  13
Code
# Canidae Temporal
tempC_modsdf_C <- tempC_modsdf %>%
   filter(D_family == "Canidae")
dim(tempC_modsdf_C)
[1] 128  13
Code
# Mustelidae Temporal
tempC_modsdf_M <- tempC_modsdf %>%
   filter(D_family == "Mustelidae")
dim(tempC_modsdf_M)
[1] 82 13

Spatial modelling procedure

Influential observations

Identify the presence of outliers or observations that may influence the models. For the spatial co-occurrence data we fit a general linear model with all covariates and interactions. We then checked for the presence of extreme data using Laverage distance plots from performance package (Lüdecke et al. 2021).

Code
# Fit model with all data
SCmods_outl <- lm(SIF ~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2, data= spatC_modsdf)

# Fit model with only felids as dominant
SCmods_outl_F <- lm(SIF ~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2, data= spatC_modsdf_F)

# Check outliers for each model
SC_out <- check_outliers(SCmods_outl)
SC_out_F <- check_outliers(SCmods_outl_F)


# Leverage plot for all data model
plot(SC_out)+
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

# Leverage plot for felidae as dominant competitor
plot(SC_out_F)+
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

Outliers of all data spatial model

Outliers of felidae dominant competior spatial model

Spatial co-occurrence leverage distance

Collinearity

We checked the collinearity of the variables used using the variance inflation factor (VIF). We consider that an VIF value > 10 indicates a high collinearity of the variables (Alain F. Zuur, Ieno, and Elphick 2010).

To calculate the VIF we use the Performance package (Lüdecke et al. 2021).

Code
#| message: false
#| warning: false
#| label: fig-Scoll
#| fig-cap: Spatial co-occurrence collinearity
#| fig-subcap: 
#|  - "VIF of all data spatial model"
#|  - "VIF of felidae dominant competior spatial model"
#| layout-ncol: 2
#| fig-width: 8

# Fit model with all data
spatC_coll <- lm(SIF ~ mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist, data= spatC_modsdf)

# Fit model with only felids as dominant
spatC_coll_F <- lm(SIF ~ mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist, data= spatC_modsdf_F)

# Check outliers for each model
spatC_colltab <- check_collinearity(spatC_coll)
spatC_colltab_F <- check_collinearity(spatC_coll_F)

# Vif plots
plot(spatC_colltab)+
  labs(subtitle = "All data Spatial model")+
  theme_bw()+
  theme(legend.position = "none",
        text=element_text(family = "Roboto"))

Code
plot(spatC_colltab_F)+
  labs(subtitle = "Felidae dominant competitor Spatial model")+
  theme_bw()+
  theme(legend.position = "none",
        text=element_text(family = "Roboto"))

Model assumptions

All data

We first check the assumptions of the model. To do this we fit the most complex model containing all available variable interactions and random factors. We then visually evaluated the normality of the residuals, linearity and homogeneity of variance using the performance package (Lüdecke et al. 2021).

Code
Spat_diag_m <-lme(SIF ~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs)^2, 
                  random = ~1|Label/Locality,
                  method = "REML",
                  data= spatC_modsdf)

Spat_diagnostic <- check_model(Spat_diag_m, 
                               check = c("homogeneity", "linearity", "qq", "normality", "reqq"))
Spat_diagnostic 

We detect deviations from assumptions. Particularly there is a kurtosis in the distribution of the residuals. There are also deviations from linearity. For that reason, we fit a T-student family glm using glmmTMB package (Brooks et al. 2017). To evaluate the GLMM we use the DHARMa package (Hartig 2021), which applies simulated residuals to evaluate the assumptions.

Code
Spat_diag_t <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2 +(1|Label/Locality),
                   data=spatC_modsdf, 
                   family=t_family(link = "identity"), 
                   REML = T)

res_t <- simulateResiduals(Spat_diag_t)
plot(res_t)

The t-family GLMM improves considerably and the graphs suggest that it meets the distribution assumptions.

Felidae

This section verifies the model assumptions considering only felids as dominant competitors.

Code
Spat_diag_m_F <-lme(SIF ~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2, 
                  random = ~1|Label/Locality,
                  method = "REML",
                  data= spatC_modsdf_F)

Spat_diagnostic_F <- check_model(Spat_diag_m_F, check = c("homogeneity", "linearity", "qq", "normality"))
Spat_diagnostic_F

Deviations from the assumptions are detected, so we tried a GLMM of family t student.

Code
Spat_diag_tF <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2 +(1|Label/Locality),
                   data=spatC_modsdf_F, 
                   family=t_family(link = "identity"), 
                   REML = T)

res_t_F <- simulateResiduals(Spat_diag_tF)
plot(res_t_F)

Since deviations from homogeneity of variance were detected, we evaluated which variables are involved in the model inadequacies.

Code
testCategorical(res_t_F, spatC_modsdf_F$diet_dist) 
testQuantiles(res_t_F, spatC_modsdf_F$mass_ratio)
testQuantiles(res_t_F, spatC_modsdf_F$Lat_abs)
testQuantiles(res_t_F, spatC_modsdf_F$p_distance)
testQuantiles(res_t_F, spatC_modsdf_F$Avg_dist)
$uniformity
$uniformity$details
catPred: Diff_diet

    One-sample Kolmogorov-Smirnov test

data:  dd[x, ]
D = 0.23074, p-value = 0.2802
alternative hypothesis: two-sided

------------------------------------------------------------ 
catPred: Same_diet

    One-sample Kolmogorov-Smirnov test

data:  dd[x, ]
D = 0.10399, p-value = 0.4252
alternative hypothesis: two-sided


$uniformity$p.value
[1] 0.2802263 0.4251758

$uniformity$p.value.cor
[1] 0.5604526 0.5604526


$homogeneity
Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  1  0.3309 0.5667
      83               

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.01022
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.09036
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.07346
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.09331
alternative hypothesis: both

Uniformity of variance test of Diet category

Uniformity of variance test of mass ratio

Uniformity of variance test of absolute latitude

Uniformity of variance test of phylogenetic distance

Uniformity of variance test of Average distance

We detected non-uniformity in the range of body mass ratio, phylogenetic distance, absolute latitude and average camera distance. Additionally, we identified that observation 84 (previously identified as outlier) does have an effect on model fit. To improve the fit, we modeled the variation of the variables by means of the dispformula term, from the glmm TMB package (Brooks et al. 2017).

Code
Spat_diag_tF2 <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2 +(1|Label/Locality),
                   dispformula = ~ mass_ratio+p_distance+Lat_abs+ Avg_dist,
                   data=spatC_modsdf_F[-84,], 
                   family=t_family(link = "identity"), 
                   REML = T)

res_t_F2 <- simulateResiduals(Spat_diag_tF2)
plot(res_t_F2)

Random structure

All data

Following the Alain F. Zuur et al. (2009a) protocol, we evaluated the relevance of the inclusion of random effects. For this we fit the previously selected model with and without the random effects (Label and Locality of each study). We selected the model with the best structure using the Akaike information criterion (AIC) with the AICcmodavg package (Mazerolle 2023).

Code
#| tbl-cap: Random-effects structure selection table for spatial co-occurrence data

# Fit model without random effects
Spat_r0 <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2,
                   data=spatC_modsdf, 
                   family=t_family(link = "identity"), 
                   REML = T)

# Fit model with label as random effect
Spat_r1 <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2 +(1|Label),
                   data=spatC_modsdf, 
                   family=t_family(link = "identity"), 
                   REML = T)

# Fit model with label and Locality as random effects
Spat_r2 <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2 +(1|Label/Locality),
                   data=spatC_modsdf, 
                   family=t_family(link = "identity"), 
                   REML = T)


# Rank the models with the AIC
spat_AICtab <- aictab(cand.set = list(Spat_r0, Spat_r1, Spat_r2),
                       modnames = c("no random",
                                    "Label random", 
                                    "Label/Locality random"),
                                    second.ord = F)

kbl(spat_AICtab, caption = "Random-effects structure selection table for spatial co-occurrence data", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Random-effects structure selection table for spatial co-occurrence data
Modnames K AIC Delta_AIC ModelLik AICWt LL Cum.Wt
2 Label random 25 293.925 0.000 1.000 0.496 -121.962 0.496
1 no random 24 294.786 0.861 0.650 0.322 -123.393 0.818
3 Label/Locality random 26 295.925 2.000 0.368 0.182 -121.962 1.000

The ?@tbl-Sraic suggests that both models with Label as random effects and without random effects are equally supported. To visualize the variation of the random parameters of each group, we use the estimate_grouplevel function of the modelbased package (Makowski et al. 2020).

Code
estimate_grouplevel(Spat_r1) %>% # Get random parameters
  plot()+  #plot
  # aesthetic changes
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

There is no significant variation from each group level in random effects. We now check the goodness of fit of these models.

Code
simulateResiduals(Spat_r1, plot = T)
simulateResiduals(Spat_r0, plot = T)
Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
 
Scaled residual values: 0.5391418 0.7377561 0.5881402 0.6518543 0.6279346 0.6963272 0.004643989 0.0760141 0.638272 0.1097375 0.7209102 0.6499179 0.8648697 0.1911011 0.9411415 0.05579266 0.8097788 0.4755805 0.8448574 0.3515596 ...
Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
 
Scaled residual values: 0.2875775 0.7883051 0.4089769 0.8830174 0.9404673 0.0455565 0.5281055 0.892419 0.551435 0.4566147 0.9568333 0.4533342 0.6775706 0.5726334 0.1029247 0.899825 0.2460877 0.04205953 0.3279207 0.9545036 ...

Gof-test of model with Label as random effects

Gof-test of model without random effects

Both models have no lack of fit. In this case, we select the simpler one (without random effects) to continue with the selection of fixed effects.

Felidae

We performed the same procedure for Felidae

Code
Spat_r0_F <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2,
                   dispformula = ~ mass_ratio+p_distance+Lat_abs+ Avg_dist,
                   data=spatC_modsdf_F[-84,], 
                   family=t_family(link = "identity"), 
                   REML = T,
                   start = list(psi = log(2.87)),
                   map = list(psi = factor(NA)))

Spat_r1_F <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2 +(1|Label),
                   dispformula = ~ mass_ratio+p_distance+Lat_abs+ Avg_dist,
                   data=spatC_modsdf_F[-84,], 
                   family=t_family(link = "identity"), 
                   REML = T,
                   start = list(psi = log(2.87)),
                   map = list(psi = factor(NA)))

Spat_r2_F <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2 +(1|Label/Locality),
                   dispformula = ~ mass_ratio+p_distance+Lat_abs+ Avg_dist,
                   data=spatC_modsdf_F[-84,], 
                   family=t_family(link = "identity"), 
                   REML = T,
                   start = list(psi = log(2.87)),
                   map = list(psi = factor(NA)))

spat_AICtab_F <- aictab(cand.set = list(Spat_r0_F, Spat_r1_F, Spat_r2_F),
                       modnames = c("no random",
                                    "Label random", 
                                    "Label/Locality random"),
                                    second.ord = F)

kbl(spat_AICtab_F, caption = "Random-effects structure selection table for spatial co-occurrence data when Felidae is dominant competitor", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Random-effects structure selection table for spatial co-occurrence data when Felidae is dominant competitor
Modnames K AIC Delta_AIC ModelLik AICWt LL Cum.Wt
no random 27 180.148 NA NA NA -63.074 NA
Label random 28 NA NA NA NA NA NA
Label/Locality random 29 183.280 NA NA NA -62.640 NA

In the case of Felidae the model selection indicates that random effects are not adequate. This is because there is no variation between Label or Locality levels.

Code
estimate_grouplevel(Spat_r1_F) %>% 
  plot()+ 
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

All label coefficient are the same for felids data

Fixed predictor selections

To select the fixed effects structure we also used the Akaike information criterion (AIC). Models with a delta AIC <2 are considered equally plausible (Burnham and Anderson 2002). Because we are going to choose the fixed effects structure, we refit the previously identified model without using the restricted maximum likelihood (REML) (Alain F. Zuur et al. 2009b). Since co-occurrence patterns may be generated by the interaction of variables, we fit all possible combinations of variables, limiting to a maximum of three parameters per model. To do this we will used the dredge function of the MuMIn package (Barton 2020).

All data

Code
# Create a global model
SC_global <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2,
                   data=spatC_modsdf, 
                   family= t_family(link = "identity"), 
                   REML = F,
                   na.action = "na.fail",
                   start = list(psi = log(1.69)),
map = list(psi = factor(NA)))

#Fit all posible combination limit to 3 parameters
SC_selec <- dredge(SC_global, rank = "AIC", m.lim= c(NA,3))
Code
kbl(SC_selec, caption = "Fixed-effects structure selection table for spatial co-occurrence data", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Fixed-effects structure selection table for spatial co-occurrence data
cond((Int)) disp((Int)) cond(Avg_dist) cond(diet_dist) cond(Lat_abs) cond(mass_ratio) cond(I(mass_ratio^2)) cond(p_distance) cond(Avg_dist:diet_dist) cond(Avg_dist:Lat_abs) cond(Avg_dist:mass_ratio) cond(Avg_dist:I(mass_ratio^2)) cond(Avg_dist:p_distance) cond(diet_dist:Lat_abs) cond(diet_dist:mass_ratio) cond(diet_dist:I(mass_ratio^2)) cond(diet_dist:p_distance) cond(Lat_abs:mass_ratio) cond(Lat_abs:p_distance) cond(mass_ratio:p_distance) cond(I(mass_ratio^2):Lat_abs) cond(I(mass_ratio^2):mass_ratio) cond(I(mass_ratio^2):p_distance) df logLik AIC delta weight
49 1.032 + NA NA NA NA -0.024 0.028 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -75.509 159.017 0.000 0.095233872
1048625 1.029 + NA NA NA NA -0.016 0.039 NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.018 5 -74.654 159.308 0.291 0.082332924
17 1.026 + NA NA NA NA -0.021 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 -76.864 159.727 0.710 0.066762335
50 1.033 + -0.009 NA NA NA -0.024 0.026 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -75.370 160.741 1.724 0.040225789
51 1.025 + NA + NA NA -0.023 0.030 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -75.476 160.952 1.935 0.036186594
57 1.030 + NA NA NA -0.006 -0.021 0.028 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -75.481 160.962 1.945 0.036005284
18 1.028 + -0.015 NA NA NA -0.022 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -76.496 160.992 1.975 0.035481985
53 1.032 + NA NA -0.002 NA -0.024 0.028 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -75.502 161.005 1.988 0.035249935
41 1.010 + NA NA NA -0.030 NA 0.026 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -76.551 161.102 2.085 0.033578960
19 1.042 + NA + NA NA -0.022 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -76.682 161.364 2.347 0.029451872
9 1.007 + NA NA NA -0.026 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 -77.728 161.457 2.440 0.028121123
131113 1.013 + NA NA NA -0.027 NA 0.023 NA NA NA NA NA NA NA NA NA NA NA -0.026 NA NA NA 5 -75.796 161.591 2.574 0.026291297
1 1.005 + NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 2 -78.829 161.659 2.642 0.025415233
25 1.025 + NA NA NA -0.004 -0.019 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -76.851 161.703 2.686 0.024868031
21 1.026 + NA NA 0.002 NA -0.021 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -76.856 161.712 2.695 0.024752479
33 1.008 + NA NA NA NA NA 0.023 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 -77.922 161.845 2.828 0.023161029
43 0.987 + NA + NA -0.031 NA 0.035 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -76.154 162.308 3.291 0.018368064
8211 1.030 + NA + NA NA -0.014 NA NA NA NA NA NA NA NA + NA NA NA NA NA NA NA 5 -76.207 162.414 3.397 0.017427872
10 1.007 + -0.018 NA NA -0.031 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -77.253 162.506 3.489 0.016639325
20 1.044 + -0.015 + NA NA -0.024 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -76.306 162.613 3.596 0.015775034
524313 1.037 + NA NA NA -0.026 -0.048 NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.015 NA 5 -76.324 162.648 3.631 0.015501177
42 1.010 + -0.013 NA NA -0.033 NA 0.024 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -76.327 162.654 3.637 0.015453356
530 1.030 + -0.012 NA NA NA -0.027 NA NA NA NA -0.008 NA NA NA NA NA NA NA NA NA NA NA 5 -76.416 162.832 3.815 0.014139679
26 1.025 + -0.017 NA NA -0.009 -0.019 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -76.427 162.854 3.837 0.013986375
45 1.010 + NA NA -0.007 -0.031 NA 0.028 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -76.472 162.943 3.926 0.013371798
22 1.028 + -0.015 NA 0.003 NA -0.022 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -76.478 162.956 3.939 0.013285763
23 1.046 + NA + -0.005 NA -0.023 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -76.655 163.310 4.293 0.011133483
262165 1.026 + NA NA -0.003 NA -0.020 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.006 NA NA 5 -76.670 163.341 4.323 0.010963681
35 0.990 + NA + NA NA NA 0.030 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -77.674 163.348 4.331 0.010921479
27 1.042 + NA + NA 0.001 -0.022 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -76.682 163.364 4.347 0.010837038
2 1.005 + -0.009 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 -78.697 163.394 4.377 0.010671899
13 1.006 + NA NA -0.002 -0.027 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -77.722 163.445 4.428 0.010407494
11 1.008 + NA + NA -0.026 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -77.726 163.452 4.435 0.010369519
5 1.005 + NA NA 0.003 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 -78.818 163.635 4.618 0.009461142
3 1.008 + NA + NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 -78.823 163.645 4.628 0.009413222
29 1.025 + NA NA 0.002 -0.003 -0.019 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -76.847 163.694 4.677 0.009185268
34 1.008 + -0.004 NA NA NA NA 0.022 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -77.897 163.795 4.778 0.008735579
37 1.008 + NA NA -0.001 NA NA 0.023 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -77.922 163.843 4.826 0.008526966
16419 0.962 + NA + NA NA NA 0.078 NA NA NA NA NA NA NA NA + NA NA NA NA NA NA 5 -76.957 163.914 4.897 0.008228560
65573 1.005 + NA NA 0.008 NA NA 0.027 NA NA NA NA NA NA NA NA NA NA 0.024 NA NA NA NA 5 -77.021 164.041 5.024 0.007722202
14 1.007 + -0.018 NA -0.002 -0.032 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -77.248 164.496 5.479 0.006151739
266 1.007 + -0.018 NA NA -0.031 NA NA NA NA -0.001 NA NA NA NA NA NA NA NA NA NA NA NA 5 -77.252 164.504 5.487 0.006126574
12 1.008 + -0.018 + NA -0.031 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -77.253 164.506 5.489 0.006123161
4107 1.009 + NA + NA -0.039 NA NA NA NA NA NA NA NA + NA NA NA NA NA NA NA NA 5 -77.421 164.842 5.825 0.005175900
39 0.985 + NA + 0.008 NA NA 0.031 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -77.602 165.204 6.187 0.004319037
32781 1.008 + NA NA -0.003 -0.026 NA NA NA NA NA NA NA NA NA NA NA 0.007 NA NA NA NA NA 5 -77.646 165.291 6.274 0.004134075
36 0.990 + -0.003 + NA NA NA 0.029 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -77.662 165.323 6.306 0.004067907
6 1.005 + -0.009 NA 0.004 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -78.678 165.356 6.339 0.004002483
4 1.007 + -0.009 + NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -78.692 165.384 6.367 0.003946027
15 1.010 + NA + -0.004 -0.027 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -77.711 165.423 6.406 0.003870416
134 1.007 + 0.001 NA 0.011 NA NA NA NA -0.017 NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -77.766 165.532 6.515 0.003664890
7 1.006 + NA + 0.002 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 -78.817 165.633 6.616 0.003484069
1058 1.009 + -0.003 NA NA NA NA 0.022 NA NA NA NA 0.002 NA NA NA NA NA NA NA NA NA NA 5 -77.894 165.788 6.771 0.003225380
38 1.008 + -0.004 NA 0.000 NA NA 0.022 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -77.897 165.795 6.778 0.003213936
2055 0.985 + NA + 0.041 NA NA NA NA NA NA NA NA + NA NA NA NA NA NA NA NA NA 5 -78.513 167.026 8.009 0.001736160
68 1.007 + -0.016 + NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -78.569 167.139 8.122 0.001641099
8 1.006 + -0.009 + 0.004 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 -78.678 167.356 8.339 0.001472433

Felidae

Note that this time the limit number of parameters in the function is 7. This is due to the number of parameters of the dispersion terms, which add 4 additional parameters.

Code
spatC_modsdf_F <- spatC_modsdf_F[-84,]

SC_global_F <- glmmTMB(formula = SIF~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Avg_dist)^2,
                   dispformula = ~ mass_ratio+p_distance+Lat_abs+ Avg_dist,
                   data=spatC_modsdf_F, 
                   family=t_family(link = "identity"), 
                   REML = F,
                   start = list(psi = log(2.87)),
                   map = list(psi = factor(NA)),
                   na.action = "na.fail")

SC_selec_F <- dredge(SC_global_F, rank = "AIC", 
                     fixed = c("disp(Avg_dist)", "disp(Lat_abs)", "disp(mass_ratio)", "disp(p_distance)"), # Mantain dispersion parameters in all models
                     m.lim= c(NA,7)) # 7 parameteres becasue we must add the dispersion terms
Code
kbl(SC_selec_F, caption = "Fixed-effects structure selection table for spatial co-occurrence data when Felidae is dominant competitor", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Fixed-effects structure selection table for spatial co-occurrence data when Felidae is dominant competitor
cond((Int)) disp((Int)) cond(Avg_dist) cond(diet_dist) cond(Lat_abs) cond(mass_ratio) cond(I(mass_ratio^2)) cond(p_distance) cond(Avg_dist:diet_dist) cond(Avg_dist:Lat_abs) cond(Avg_dist:mass_ratio) cond(Avg_dist:I(mass_ratio^2)) cond(Avg_dist:p_distance) cond(diet_dist:Lat_abs) cond(diet_dist:mass_ratio) cond(diet_dist:I(mass_ratio^2)) cond(diet_dist:p_distance) cond(Lat_abs:mass_ratio) cond(Lat_abs:p_distance) cond(mass_ratio:p_distance) cond(I(mass_ratio^2):Lat_abs) cond(I(mass_ratio^2):mass_ratio) cond(I(mass_ratio^2):p_distance) disp(Avg_dist) disp(Lat_abs) disp(mass_ratio) disp(p_distance) df logLik AIC delta weight
262165 1.041 -1.609 NA NA -0.001 NA -0.107 NA NA NA NA NA NA NA NA NA NA NA NA NA -0.067 NA NA -0.033 0.109 0.024 -0.183 9 -29.918 77.836 0.000 0.106482503
21 0.995 -1.574 NA NA -0.041 NA -0.034 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.036 0.147 0.025 -0.138 8 -31.103 78.206 0.370 0.088479291
17 1.018 -1.581 NA NA NA NA -0.030 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.038 0.127 0.018 -0.086 7 -32.233 78.466 0.630 0.077718447
1048625 1.011 -1.613 NA NA NA NA -0.016 0.024 NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.024 0.096 0.125 -0.053 -0.068 9 -30.878 79.756 1.920 0.040774185
22 0.997 -1.584 -0.019 NA -0.043 NA -0.036 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.038 0.146 0.033 -0.151 9 -30.971 79.943 2.107 0.037134205
53 0.995 -1.576 NA NA -0.041 NA -0.034 0.009 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.038 0.159 0.033 -0.146 9 -31.035 80.069 2.233 0.034858667
23 1.011 -1.575 NA + -0.046 NA -0.034 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.039 0.148 0.024 -0.148 9 -31.066 80.132 2.296 0.033781932
19 0.987 -1.577 NA + NA NA -0.030 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.019 0.135 0.025 -0.092 8 -32.079 80.157 2.321 0.033358046
29 0.995 -1.574 NA NA -0.041 0.000 -0.034 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.035 0.147 0.025 -0.138 9 -31.103 80.206 2.370 0.032549878
25 1.023 -1.589 NA NA NA 0.018 -0.037 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.017 0.125 0.019 -0.104 8 -32.108 80.216 2.380 0.032398022
524313 1.050 -1.598 NA NA NA -0.009 -0.091 NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.023 NA 0.034 0.104 0.042 -0.120 9 -31.185 80.369 2.533 0.030005702
18 1.019 -1.590 -0.012 NA NA NA -0.031 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.052 0.118 0.023 -0.088 8 -32.185 80.370 2.534 0.029989393
49 1.020 -1.584 NA NA NA NA -0.031 0.007 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.039 0.132 0.023 -0.092 8 -32.189 80.379 2.543 0.029863756
530 1.047 -1.604 0.040 NA NA NA -0.080 NA NA NA NA -0.064 NA NA NA NA NA NA NA NA NA NA NA 0.100 0.084 0.028 -0.111 9 -31.241 80.482 2.646 0.028365000
13 0.962 -1.519 NA NA -0.049 -0.048 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.052 0.147 0.013 -0.065 8 -32.453 80.906 3.070 0.022942770
1 0.982 -1.543 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.047 0.099 0.015 0.004 6 -34.498 80.997 3.161 0.021923939
9 0.990 -1.537 NA NA NA -0.032 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.102 0.113 -0.003 0.001 7 -33.736 81.472 3.636 0.017286222
32781 0.983 -1.550 NA NA -0.044 -0.014 NA NA NA NA NA NA NA NA NA NA NA 0.044 NA NA NA NA NA 0.103 0.114 0.015 -0.063 9 -31.806 81.612 3.777 0.016113987
5 0.963 -1.527 NA NA -0.032 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.023 0.135 0.039 -0.042 7 -33.864 81.729 3.893 0.015203657
51 0.976 -1.585 NA + NA NA -0.031 0.014 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.017 0.146 0.038 -0.104 9 -31.922 81.843 4.008 0.014356678
8211 0.967 -1.573 NA + NA NA -0.016 NA NA NA NA NA NA NA NA + NA NA NA NA NA NA NA 0.027 0.146 -0.006 -0.094 9 -31.922 81.845 4.009 0.014348124
2055 0.880 -1.546 NA + 0.167 NA NA NA NA NA NA NA NA + NA NA NA NA NA NA NA NA NA 0.041 0.156 0.083 -0.067 9 -31.953 81.907 4.071 0.013909338
27 0.997 -1.584 NA + NA 0.013 -0.035 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.010 0.132 0.025 -0.103 9 -32.020 82.040 4.204 0.013010901
20 0.989 -1.585 -0.011 + NA NA -0.031 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.031 0.128 0.029 -0.095 9 -32.040 82.080 4.244 0.012756341
3 0.927 -1.533 NA + NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.031 0.120 0.010 0.008 7 -34.074 82.148 4.312 0.012327659
57 1.023 -1.591 NA NA NA 0.016 -0.037 0.005 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.021 0.128 0.023 -0.107 9 -32.083 82.167 4.331 0.012213911
14 0.957 -1.533 -0.040 NA -0.059 -0.064 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.031 0.157 0.032 -0.088 9 -32.091 82.183 4.347 0.012116875
26 1.023 -1.591 -0.004 NA NA 0.016 -0.037 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.024 0.122 0.021 -0.103 9 -32.104 82.208 4.372 0.011966312
50 1.020 -1.591 -0.011 NA NA NA -0.032 0.006 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.051 0.124 0.027 -0.093 9 -32.154 82.307 4.471 0.011386440
11 0.933 -1.530 NA + NA -0.032 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.070 0.132 0.003 -0.007 8 -33.306 82.611 4.775 0.009780307
45 0.962 -1.521 NA NA -0.051 -0.051 NA 0.011 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.047 0.167 0.025 -0.083 9 -32.361 82.723 4.887 0.009248308
15 0.946 -1.519 NA + -0.045 -0.047 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.050 0.147 0.012 -0.057 9 -32.415 82.830 4.994 0.008768419
2 0.983 -1.535 0.012 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.037 0.104 0.004 0.004 7 -34.451 82.901 5.065 0.008460080
16419 0.538 -1.580 NA + NA NA NA 0.467 NA NA NA NA NA NA NA NA + NA NA NA NA NA NA 0.121 0.128 0.080 -0.021 9 -32.469 82.939 5.103 0.008302923
33 0.982 -1.542 NA NA NA NA NA -0.002 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.048 0.096 0.012 0.008 7 -34.494 82.987 5.151 0.008103121
266 1.008 -1.589 0.007 NA NA -0.007 NA NA NA NA 0.063 NA NA NA NA NA NA NA NA NA NA NA NA 0.113 0.101 0.032 -0.072 9 -32.588 83.177 5.341 0.007370482
10 0.990 -1.545 -0.015 NA NA -0.036 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.115 0.107 0.004 0.003 8 -33.681 83.362 5.527 0.006717325
41 0.992 -1.538 NA NA NA -0.032 NA 0.004 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.100 0.118 0.000 -0.003 8 -33.726 83.451 5.615 0.006426230
7 0.933 -1.525 NA + -0.025 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.011 0.136 0.026 -0.021 8 -33.739 83.478 5.642 0.006340809
131113 1.002 -1.543 NA NA NA -0.037 NA 0.004 NA NA NA NA NA NA NA NA NA NA NA -0.042 NA NA NA 0.197 0.090 -0.084 0.056 9 -32.746 83.492 5.657 0.006294670
6 0.963 -1.523 0.008 NA -0.031 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.018 0.134 0.030 -0.038 8 -33.843 83.686 5.850 0.005713972
37 0.963 -1.527 NA NA -0.032 NA NA 0.001 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.024 0.136 0.041 -0.044 8 -33.864 83.727 5.891 0.005597270
35 0.919 -1.538 NA + NA NA NA 0.010 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.022 0.131 0.020 -0.007 8 -34.004 84.008 6.172 0.004864229
4 0.926 -1.527 0.012 + NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.025 0.124 0.002 0.007 8 -34.027 84.055 6.219 0.004751913
43 0.917 -1.537 NA + NA -0.036 NA 0.019 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.050 0.156 0.022 -0.031 9 -33.076 84.152 6.316 0.004526128
4107 0.932 -1.532 NA + NA -0.053 NA NA NA NA NA NA NA NA + NA NA NA NA NA NA NA NA 0.064 0.127 0.015 -0.001 9 -33.190 84.380 6.544 0.004039537
12 0.933 -1.538 -0.016 + NA -0.037 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.078 0.127 0.008 -0.006 9 -33.240 84.480 6.644 0.003842679
134 0.974 -1.576 -0.024 NA -0.028 NA NA NA NA -0.071 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.266 0.074 0.049 -0.047 9 -33.327 84.653 6.817 0.003522759
34 0.982 -1.535 0.012 NA NA NA NA -0.001 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.038 0.103 0.003 0.005 8 -34.450 84.899 7.063 0.003115193
42 0.991 -1.545 -0.014 NA NA -0.036 NA 0.002 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.113 0.110 0.005 0.000 9 -33.677 85.353 7.517 0.002482502
39 0.927 -1.527 NA + -0.024 NA NA 0.007 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.015 0.146 0.033 -0.031 9 -33.703 85.406 7.570 0.002417765
8 0.932 -1.521 0.009 + -0.024 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.006 0.136 0.017 -0.018 9 -33.709 85.417 7.581 0.002404586
65573 0.961 -1.528 NA NA -0.036 NA NA -0.004 NA NA NA NA NA NA NA NA NA NA -0.009 NA NA NA NA -0.048 0.145 0.042 -0.047 9 -33.809 85.617 7.781 0.002175595
38 0.963 -1.524 0.008 NA -0.031 NA NA 0.001 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.020 0.136 0.032 -0.040 9 -33.841 85.683 7.847 0.002105420
36 0.918 -1.531 0.014 + NA NA NA 0.012 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.015 0.138 0.013 -0.009 9 -33.935 85.870 8.034 0.001917204
68 0.926 -1.521 0.038 + NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.007 0.130 0.000 0.009 9 -33.992 85.985 8.149 0.001810560
1058 0.984 -1.520 0.023 NA NA NA NA -0.002 NA NA NA NA 0.021 NA NA NA NA NA NA NA NA NA NA 0.020 0.116 -0.023 0.016 9 -34.341 86.682 8.846 0.001277834

Confidence intervals explorations

Consistent with the model selection strategy (AIC) and to avoid uninformative variables, we explored the 85% confidence intervals of the regression coefficients of the best models (Sutherland et al. 2023). Variables whose 85% CI overlap 0 are considered as uninformative and therefore not included in the inference (Arnold 2010).

Code
# Function to get 85%IC
get_ci <- function(mod_name, mods){
  ci_df <- parameters::model_parameters(mods, ci = 0.85) %>% 
    select(Parameter, Coefficient, CI_low, CI_high, Component) %>% 
    filter(Component == "conditional") %>% 
    filter(Parameter != "(Intercept)") %>%
    mutate(Model = mod_name,
           Informative = case_when(
    CI_low < 0 & CI_high < 0 ~ "yes",
    CI_low > 0 & CI_high > 0 ~ "yes",
    TRUE ~ "no")) 
  return(ci_df)   
}

# Function to plot

ci_plot <- function(ci_df){
ggplot(ci_df, aes(x=Coefficient, y= Parameter))+
  geom_pointrange(aes(xmin=CI_low, xmax= CI_high,
                      col= Model, linetype= Informative),
                  position = position_dodge2(0.5), linewidth= 1)+
  scale_linetype_manual(values = c("no"="dashed", "yes"= "solid"))+
  geom_vline(xintercept = 0, linetype= "dashed")+
  scale_color_viridis_d()+
  labs(caption = "estimates with 85% ci intervals",
       col= "Model ID")+
  theme_bw()+
    theme(text=element_text(family = "Roboto"))
  
}
Code
# get best models for all data 
SC_best_mods <- get.models(SC_selec, subset = delta <2)
# get best models for felidae subset data
SC_best_mods_F <- get.models(SC_selec_F, subset = delta <2)

# Apply the function to obtain the table of coefficients of selected the models
SC_best_ci <- map2_df(names(SC_best_mods), SC_best_mods, get_ci) 
SC_best_ci_F <- map2_df(names(SC_best_mods_F), SC_best_mods_F, get_ci) 

ci_plot(SC_best_ci)+ labs(title= "All data")
ci_plot(SC_best_ci_F)+ labs(title= "Felidae dominant competitor")

All data best model 85% CI

Felidae data best model 85% CI

Temporal modelling procedure

Influential observations

Identify the presence of outliers or observations that may influence the models. For the temporal co-ocurrence data we fit a beta family generalized linear model with all covariates and interactions (Cribari-Neto and Zeileis 2010). We then checked for the presence of extreme observations using Cook’s distance plots from performance package (Lüdecke et al. 2021).

Code
# Models for each data
TCmods_outl <- betareg(Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2, data= tempC_modsdf)

TCmods_outl_F <- betareg(Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2, data= tempC_modsdf_F)

TCmods_outl_C <-betareg(Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2, data= tempC_modsdf_C)

TCmods_outl_M <- betareg(Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2, data= tempC_modsdf_M)

#Check outliers
TC_out <- check_outliers(TCmods_outl)
TC_out_F <- check_outliers(TCmods_outl_F)
TC_out_C <- check_outliers(TCmods_outl_C)
TC_out_M <- check_outliers(TCmods_outl_M)

# Cook's distance plots
plot(TC_out)+
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

plot(TC_out_F)+
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

plot(TC_out_C)+
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

plot(TC_out_M)+
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

Outliers of all data temporal model

Outliers of Felidae dominant competior Temporal model

Outliers of Celidae dominant competior Temporal model

Outliers of Mustelidae dominant competior Temporal model

Temporal co-occurrence cook distance distance

A possible outlier was detected for the Mustelidae data as a dominant competitor. It corresponds to observation 27 which exceeded the 0.98 Cook’s distance threshold.

Collinearity

We checked the collinearity of the variables used using the variance inflation factor (VIF). We consider that an VIF value > 10 indicates a high collinearity of the variables (Alain F. Zuur, Ieno, and Elphick 2010).

To calculate the VIF we use the Performance package (Lüdecke et al. 2021).

Code
# Fit models
tempC_coll <- betareg(Ov_coeff ~ mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur, data= tempC_modsdf)
tempC_coll_F <- betareg(Ov_coeff ~ mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur, data= tempC_modsdf_F)
tempC_coll_C <- betareg(Ov_coeff ~ mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur, data= tempC_modsdf_C)
tempC_coll_M <- betareg(Ov_coeff ~ mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur, data= tempC_modsdf_M)

# Check collinearity
tempC_colltab <- check_collinearity(tempC_coll)
tempC_colltab_F <- check_collinearity(tempC_coll_F)
tempC_colltab_C <- check_collinearity(tempC_coll_C)
tempC_colltab_M <- check_collinearity(tempC_coll_M )


# Vif plots
plot(tempC_colltab)+
  labs(subtitle = "All data Temporal model")+
  theme_bw()+
  theme(legend.position = "none",
        text=element_text(family = "Roboto"))

plot(tempC_colltab_F)+
  labs(subtitle = "Felidae Temporal model")+
  theme_bw()+
  theme(legend.position = "none",
        text=element_text(family = "Roboto"))

plot(tempC_colltab_C)+
  labs(subtitle = "Canidae Temporal model")+
  theme_bw()+
  theme(legend.position = "none",
        text=element_text(family = "Roboto"))

plot(tempC_colltab_M)+
  labs(subtitle = "Mustelidae Temporal model")+
  theme_bw()+
  theme(legend.position = "none",
        text=element_text(family = "Roboto"))

(a) VIF of all data model

(b) VIF of Felidae model

(c) VIF of Canidae model

(d) VIF of Mustelidae model

Figure 3: Outliers model detection temporal models

Model assumptions

We verify the model assumptions by visual inspection of the simulated residuals from the DHARMa package (Hartig 2021). To do so we fit the more complex model which includes fixed variables and their interactions, as well as random effects.

All data

Code
Temp_diag <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label/Locality),
                   data=tempC_modsdf, 
                   family=beta_family(), REML = T)

Temp_diag_res <- simulateResiduals(Temp_diag)
plot(Temp_diag_res)

Since deviations from homogeneity of variance were detected, we evaluated which variables are involved in the model inadequacies.

Code
testCategorical(Temp_diag_res, tempC_modsdf$diet_dist) 
testQuantiles(Temp_diag_res , tempC_modsdf$mass_ratio)
testQuantiles(Temp_diag_res , tempC_modsdf$Lat_abs)
testQuantiles(Temp_diag_res , tempC_modsdf$p_distance)
testQuantiles(Temp_diag_res , tempC_modsdf$Samp_dur)
$uniformity
$uniformity$details
catPred: Diff_diet

    One-sample Kolmogorov-Smirnov test

data:  dd[x, ]
D = 0.091409, p-value = 0.01375
alternative hypothesis: two-sided

------------------------------------------------------------ 
catPred: Same_diet

    One-sample Kolmogorov-Smirnov test

data:  dd[x, ]
D = 0.058897, p-value = 0.1027
alternative hypothesis: two-sided


$uniformity$p.value
[1] 0.01374834 0.10265831

$uniformity$p.value.cor
[1] 0.02749668 0.10265831


$homogeneity
Levene's Test for Homogeneity of Variance (center = median)
       Df F value Pr(>F)
group   1       0 0.9949
      724               

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.1531
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value < 2.2e-16
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.01388
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value < 2.2e-16
alternative hypothesis: both

Uniformity of variance test of Diet category

Uniformity of variance test of mass ratio

Uniformity of variance test of absolute latitude

Uniformity of variance test of phylogenetic distance

Uniformity of variance test of sampling duration

We detected non-uniformity in the range of diet distance, phylogenetic distance, absolute latitude and mean camera distance. Additionally, we identified that observation 84 (previously identified as outlier) does have an effect on model fit. To improve the fit, we modeled the variation of the variables by means of the dispformula term, from the glmm TMB package (Brooks et al. 2017).

Code
Temp_diag2 <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label/Locality),
                      dispformula = ~diet_dist+ p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf, 
                   family=beta_family(), REML = T)

Temp_diag_res2 <- simulateResiduals(Temp_diag2)
plot(Temp_diag_res2)

Felidae

Code
Temp_diag_F <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label/Locality),
                   data=tempC_modsdf_F, 
                   family=beta_family(), REML = T)

Temp_diag_res_F <- simulateResiduals(Temp_diag_F)
plot(Temp_diag_res_F)

Code
testCategorical(Temp_diag_F, tempC_modsdf_F$diet_dist)
testQuantiles(Temp_diag_F, tempC_modsdf_F$mass_ratio)
testQuantiles(Temp_diag_F, tempC_modsdf_F$Lat_abs)
testQuantiles(Temp_diag_F, tempC_modsdf_F$p_distance)
testQuantiles(Temp_diag_F, tempC_modsdf_F$Samp_dur)
$uniformity
$uniformity$details
catPred: Diff_diet

    One-sample Kolmogorov-Smirnov test

data:  dd[x, ]
D = 0.090667, p-value = 0.45
alternative hypothesis: two-sided

------------------------------------------------------------ 
catPred: Same_diet

    One-sample Kolmogorov-Smirnov test

data:  dd[x, ]
D = 0.051049, p-value = 0.4453
alternative hypothesis: two-sided


$uniformity$p.value
[1] 0.4500480 0.4453188

$uniformity$p.value.cor
[1] 0.8906377 0.8906377


$homogeneity
Levene's Test for Homogeneity of Variance (center = median)
       Df F value Pr(>F)
group   1  0.5373  0.464
      374               

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.07165
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.1042
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.0005894
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.00368
alternative hypothesis: both

Uniformity of variance test of Diet category

Uniformity of variance test of mass ratio

Uniformity of variance test of absolute latitude

Uniformity of variance test of phylogenetic distance

Uniformity of variance test of Sampling duration

Code
Temp_diag_F2 <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label/Locality),
                      dispformula = ~mass_ratio+p_distance+Lat_abs+Samp_dur,
                   data=tempC_modsdf_F, 
                   family=beta_family(), REML = T)

Temp_diag_res_F2 <- simulateResiduals(Temp_diag_F2)
plot(Temp_diag_res_F2)

Canidae

Code
Temp_diag_C <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label/Locality),
                   data=tempC_modsdf_C, 
                   family=beta_family(), REML = T)

Temp_diag_res_C <- simulateResiduals(Temp_diag_C)
plot(Temp_diag_res_C)

Code
testCategorical(Temp_diag_C, tempC_modsdf_C$diet_dist)
testQuantiles(Temp_diag_C, tempC_modsdf_C$mass_ratio)
testQuantiles(Temp_diag_C, tempC_modsdf_C$Lat_abs)
testQuantiles(Temp_diag_C, tempC_modsdf_C$p_distance)
testQuantiles(Temp_diag_C, tempC_modsdf_C$Samp_dur)
$uniformity
$uniformity$details
catPred: Diff_diet

    One-sample Kolmogorov-Smirnov test

data:  dd[x, ]
D = 0.16209, p-value = 0.05327
alternative hypothesis: two-sided

------------------------------------------------------------ 
catPred: Same_diet

    One-sample Kolmogorov-Smirnov test

data:  dd[x, ]
D = 0.081559, p-value = 0.8274
alternative hypothesis: two-sided


$uniformity$p.value
[1] 0.05326729 0.82741826

$uniformity$p.value.cor
[1] 0.1065346 0.8274183


$homogeneity
Levene's Test for Homogeneity of Variance (center = median)
       Df F value  Pr(>F)  
group   1  2.9441 0.08865 .
      126                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.2533
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value < 2.2e-16
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.3189
alternative hypothesis: both

    Test for location of quantiles via qgam

data:  simulationOutput
p-value = 0.03583
alternative hypothesis: both

Uniformity of variance test of Diet category

Uniformity of variance test of mass ratio

Uniformity of variance test of absolute latitude

Uniformity of variance test of phylogenetic distance

Uniformity of variance test of Sampling duration

Code
Temp_diag_C2 <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label/Locality),
                      dispformula = ~Samp_dur+Lat_abs,
                   data=tempC_modsdf_C, 
                   family=beta_family(), REML = T)

Temp_diag_res_C2 <- simulateResiduals(Temp_diag_C2)
plot(Temp_diag_res_C2)

Mustelidae

Code
Temp_diag_M <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label/Locality),
                   data=tempC_modsdf_M, 
                   family=beta_family(), REML = T)

Temp_diag_res_M <- simulateResiduals(Temp_diag_M)
plot(Temp_diag_res_M)

The previously identified outlier caused the inadequacies of the model.

Code
Temp_diag_M2 <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label/Locality),
                      data=tempC_modsdf_M[-27,], 
                   family=beta_family(), REML = T)

Temp_diag_res_M2 <- simulateResiduals(Temp_diag_M2)
plot(Temp_diag_res_M2)

Random structure

Following the Alain F. Zuur et al. (2009a) protocol, we evaluated the relevance of the inclusion of random effects. For this we fit the previously selected model with and without the random effects (Label and Locality of each study). We selected the model with the best structure using the Akaike information criterion (AIC) with the AICcmodavg package (Mazerolle 2023).

All data

Code
Temp_r0 <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2,
                   dispformula = ~diet_dist+ p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf, 
                   family=beta_family(), 
                   REML = T)

Temp_r1 <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2 +(1|Label),
                   dispformula = ~diet_dist+ p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf, 
                   family=beta_family(), 
                   REML = T)

Temp_r2 <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2 +(1|Label/Locality),
                   dispformula = ~diet_dist+ p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf, 
                   family=beta_family(), 
                   REML = T)


temp_AICtab <- aictab(cand.set = list(Temp_r0, Temp_r1, Temp_r2),
                       modnames = c("no random",
                                    "Label random", 
                                    "Label/Locality random"),
                                    second.ord = F)

kbl(temp_AICtab, caption = "Random-effects structure selection table for Temporal co-occurrence data", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Random-effects structure selection table for Temporal co-occurrence data
Modnames K AIC Delta_AIC ModelLik AICWt LL Cum.Wt
2 Label random 28 -421.278 0.000 1.000 0.731 238.639 0.731
3 Label/Locality random 29 -419.278 2.000 0.368 0.269 238.639 1.000
1 no random 27 -342.472 78.807 0.000 0.000 198.236 1.000
Code
estimate_grouplevel(Temp_r1) %>% # Get random parameters
  plot()+  #plot
  # aesthetic changes
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

Felidae

Code
Temp_r0_F <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2,
                   data=tempC_modsdf_F, 
                   family=beta_family(), 
                   REML = T)

Temp_r1_F <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2 +(1|Label),
                   data=tempC_modsdf_F, 
                   family=beta_family(), 
                   REML = T)

Temp_r2_F <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2 +(1|Label/Locality),
                   data=tempC_modsdf_F, 
                   family=beta_family(), 
                   REML = T)


temp_AICtab_F <- aictab(cand.set = list(Temp_r0_F, Temp_r1_F, Temp_r2_F),
                       modnames = c("no random",
                                    "Label random", 
                                    "Label/Locality random"),
                                    second.ord = F)


kbl(temp_AICtab_F, caption = "Random-effects structure selection table for Temporal co-occurrence data when Felidae is dominant competitor", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Random-effects structure selection table for Temporal co-occurrence data when Felidae is dominant competitor
Modnames K AIC Delta_AIC ModelLik AICWt LL Cum.Wt
2 Label random 24 -220.705 0.000 1.000 0.731 134.352 0.731
3 Label/Locality random 25 -218.705 2.000 0.368 0.269 134.352 1.000
1 no random 23 -177.528 43.177 0.000 0.000 111.764 1.000
Code
estimate_grouplevel(Temp_r1_F) %>% # Get random parameters
  plot()+  #plot
  # aesthetic changes
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

Canidae

Code
Temp_r0_C <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2,
                   data=tempC_modsdf_C, 
                   family=beta_family(), 
                   REML = T)

Temp_r1_C <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2 +(1|Label),
                   data=tempC_modsdf_C, 
                   family=beta_family(), 
                   REML = T)

Temp_r2_C <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2 +(1|Label/Locality),
                   data=tempC_modsdf_C, 
                   family=beta_family(), 
                   REML = T)


temp_AICtab_C <- aictab(cand.set = list(Temp_r0_C, Temp_r1_C, Temp_r2_C),
                       modnames = c("no random",
                                    "Label random", 
                                    "Label/Locality random"),
                                    second.ord = F)

kbl(temp_AICtab_C, caption = "Random-effects structure selection table for Temporal co-occurrence data when Canidae is dominant competitor", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Random-effects structure selection table for Temporal co-occurrence data when Canidae is dominant competitor
Modnames K AIC Delta_AIC ModelLik AICWt LL Cum.Wt
2 Label random 24 -59.934 0.000 1.000 0.726 53.967 0.726
3 Label/Locality random 25 -57.934 2.000 0.368 0.267 53.967 0.994
1 no random 23 -50.482 9.451 0.009 0.006 48.241 1.000
Code
estimate_grouplevel(Temp_r1_C) %>% # Get random parameters
  plot()+  #plot
  # aesthetic changes
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

Mustelidae

Code
Temp_r0_M <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2,
                   data=tempC_modsdf_M, 
                   family=beta_family(), 
                   REML = T)

Temp_r1_M <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2 +(1|Label),
                   data=tempC_modsdf_M, 
                   family=beta_family(), 
                   REML = T)

Temp_r2_M <- glmmTMB(formula = Ov_coeff~ (mass_ratio+ I(mass_ratio^2)+ p_distance+ diet_dist+ Lat_abs+ Samp_dur)^2 +(1|Label/Locality),
                   data=tempC_modsdf_M, 
                   family=beta_family(), 
                   REML = T)


temp_AICtab_M <- aictab(cand.set = list(Temp_r0_M, Temp_r1_M, Temp_r2_M),
                       modnames = c("no random",
                                    "Label random", 
                                    "Label/Locality random"),
                                    second.ord = F)
kbl(temp_AICtab_M, caption = "Random-effects structure selection table for Temporal co-occurrence data when Mustelidae is dominant competitor", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Random-effects structure selection table for Temporal co-occurrence data when Mustelidae is dominant competitor
Modnames K AIC Delta_AIC ModelLik AICWt LL Cum.Wt
no random 23 -45.204 0.000 1.000 0.473 45.602 0.473
Label random 24 -44.774 0.430 0.806 0.381 46.387 0.854
Label/Locality random 25 -42.861 2.343 0.310 0.146 46.431 1.000
Code
estimate_grouplevel(Temp_r1_M) %>% # Get random parameters
  plot()+  #plot
  # aesthetic changes
  theme_bw()+
  theme(text=element_text(family = "Roboto"))

Fixed predictor selections

All data

Code
TC_global <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label),
                      dispformula = ~p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf, 
                   family=beta_family(), REML = F,
                   na.action = "na.fail")

TC_selec <- dredge(TC_global, rank = "AIC", 
                   fixed = c("disp(p_distance)","disp(Lat_abs)","disp(Samp_dur)"), 
                   m.lim= c(NA,6))
Code
kbl(TC_selec, caption = "Fixed-effects structure selection table for temporal co-occurrence data", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Fixed-effects structure selection table for temporal co-occurrence data
cond((Int)) disp((Int)) cond(diet_dist) cond(Lat_abs) cond(mass_ratio) cond(I(mass_ratio^2)) cond(p_distance) cond(Samp_dur) cond(diet_dist:Lat_abs) cond(diet_dist:mass_ratio) cond(diet_dist:I(mass_ratio^2)) cond(diet_dist:p_distance) cond(diet_dist:Samp_dur) cond(Lat_abs:mass_ratio) cond(Lat_abs:p_distance) cond(Lat_abs:Samp_dur) cond(mass_ratio:p_distance) cond(mass_ratio:Samp_dur) cond(I(mass_ratio^2):Lat_abs) cond(I(mass_ratio^2):mass_ratio) cond(I(mass_ratio^2):p_distance) cond(I(mass_ratio^2):Samp_dur) cond(p_distance:Samp_dur) disp(Lat_abs) disp(p_distance) disp(Samp_dur) df logLik AIC delta weight
23 0.692 1.940 NA 0.130 -0.069 NA -0.109 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.319 -0.277 0.016 9 278.693 -539.385 0.000 3.682725e-01
27 0.736 1.939 NA 0.126 NA -0.038 -0.110 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.314 -0.288 0.022 9 278.004 -538.008 1.378 1.849448e-01
262169 0.780 1.954 NA NA NA -0.062 -0.148 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.072 NA NA 0.276 -0.300 0.001 9 277.762 -537.525 1.861 1.452491e-01
19 0.703 1.936 NA 0.132 NA NA -0.116 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.316 -0.281 0.017 8 276.098 -536.196 3.190 7.474154e-02
4115 0.696 1.937 NA 0.136 NA NA -0.119 NA NA NA NA NA NA NA 0.032 NA NA NA NA NA NA NA NA 0.324 -0.290 0.014 9 276.573 -535.146 4.240 4.421392e-02
20 0.707 1.936 + 0.131 NA NA -0.117 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.315 -0.281 0.017 9 276.102 -534.204 5.182 2.760539e-02
51 0.703 1.936 NA 0.132 NA NA -0.116 0.004 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.316 -0.281 0.017 9 276.100 -534.200 5.185 2.755787e-02
21 0.727 1.946 NA NA -0.069 NA -0.099 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.286 -0.278 0.007 8 274.888 -533.776 5.609 2.229337e-02
25 0.772 1.944 NA NA NA -0.041 -0.100 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.281 -0.289 0.014 8 274.454 -532.909 6.477 1.444788e-02
29 0.749 1.946 NA NA -0.050 -0.024 -0.098 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.285 -0.283 0.011 9 275.429 -532.859 6.527 1.409054e-02
16405 0.730 1.946 NA NA -0.066 NA -0.103 NA NA NA NA NA NA NA NA NA -0.019 NA NA NA NA NA NA 0.286 -0.281 0.009 9 275.028 -532.056 7.330 9.429858e-03
22 0.738 1.946 + NA -0.069 NA -0.103 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.284 -0.277 0.007 9 274.931 -531.863 7.523 8.562394e-03
53 0.726 1.946 NA NA -0.069 NA -0.099 -0.001 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.286 -0.278 0.007 9 274.888 -531.776 7.609 8.201678e-03
26 0.782 1.944 + NA NA -0.040 -0.104 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.280 -0.289 0.014 9 274.489 -530.977 8.408 5.500218e-03
57 0.771 1.944 NA NA NA -0.040 -0.100 -0.006 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.281 -0.289 0.014 9 274.459 -530.917 8.468 5.337675e-03
7 0.717 1.929 NA 0.111 -0.077 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.309 -0.232 0.022 8 273.406 -530.812 8.573 5.063611e-03
17 0.739 1.942 NA NA NA NA -0.106 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.282 -0.282 0.009 7 272.331 -530.662 8.723 4.698662e-03
8 0.668 1.929 + 0.118 -0.077 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.319 -0.240 0.024 9 274.107 -530.214 9.172 3.754212e-03
15 0.741 1.930 NA 0.108 -0.058 -0.024 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.308 -0.239 0.026 9 273.944 -529.887 9.498 3.189359e-03
11 0.769 1.928 NA 0.106 NA -0.043 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.304 -0.244 0.030 8 272.614 -529.228 10.158 2.293413e-03
2055 0.718 1.929 NA 0.110 -0.076 NA NA NA NA NA NA NA NA -0.007 NA NA NA NA NA NA NA NA NA 0.310 -0.233 0.022 9 273.434 -528.868 10.517 1.915846e-03
39 0.718 1.929 NA 0.112 -0.078 NA NA 0.007 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.310 -0.233 0.023 9 273.414 -528.827 10.558 1.877340e-03
18 0.753 1.942 + NA NA NA -0.111 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.280 -0.282 0.008 8 272.389 -528.777 10.608 1.830975e-03
12 0.717 1.928 + 0.114 NA -0.044 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.314 -0.252 0.032 9 273.381 -528.762 10.623 1.817263e-03
49 0.738 1.942 NA NA NA NA -0.106 -0.009 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.282 -0.282 0.007 8 272.343 -528.686 10.699 1.749070e-03
65547 0.772 1.929 NA 0.087 NA -0.044 NA NA NA NA NA NA NA NA NA NA NA NA 0.021 NA NA NA NA 0.300 -0.245 0.026 9 273.149 -528.298 11.087 1.441001e-03
43 0.769 1.928 NA 0.107 NA -0.044 NA 0.001 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.304 -0.244 0.030 9 272.614 -527.228 12.157 8.438028e-04
5 0.745 1.933 NA NA -0.077 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.280 -0.236 0.015 7 270.570 -527.141 12.245 8.078074e-04
134 0.726 1.939 + NA -0.137 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA 0.281 -0.248 0.015 9 272.520 -527.040 12.346 7.679280e-04
50 0.752 1.942 + NA NA NA -0.111 -0.010 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.280 -0.281 0.007 9 272.402 -526.804 12.581 6.827013e-04
530 0.753 1.942 + NA NA NA -0.111 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA 0.280 -0.282 0.008 9 272.389 -526.777 12.608 6.735863e-04
1048625 0.738 1.942 NA NA NA NA -0.106 -0.006 NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.009 0.281 -0.280 0.008 9 272.387 -526.774 12.611 6.724561e-04
13 0.770 1.934 NA NA -0.055 -0.026 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.279 -0.244 0.019 8 271.228 -526.456 12.930 5.734858e-04
3 0.732 1.924 NA 0.112 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.304 -0.231 0.024 7 270.142 -526.284 13.102 5.262371e-04
9 0.796 1.932 NA NA NA -0.045 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.276 -0.248 0.022 7 270.032 -526.064 13.322 4.714157e-04
6 0.711 1.934 + NA -0.076 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.285 -0.242 0.016 8 270.938 -525.876 13.509 4.291877e-04
4 0.681 1.924 + 0.119 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.314 -0.240 0.026 8 270.881 -525.762 13.624 4.053632e-04
131085 0.789 1.936 NA NA -0.080 -0.060 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.016 NA NA NA 0.281 -0.249 0.017 9 271.696 -525.392 13.993 3.369221e-04
14 0.736 1.935 + NA -0.054 -0.027 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.284 -0.249 0.020 9 271.619 -525.238 14.147 3.120123e-04
37 0.745 1.933 NA NA -0.077 NA NA -0.004 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.280 -0.236 0.014 8 270.572 -525.145 14.241 2.977345e-04
10 0.760 1.932 + NA NA -0.045 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.281 -0.254 0.024 8 270.454 -524.908 14.477 2.645740e-04
68 0.699 1.928 + 0.088 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.317 -0.239 0.031 9 271.258 -524.516 14.869 2.174211e-04
45 0.770 1.934 NA NA -0.055 -0.026 NA -0.004 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.279 -0.243 0.018 9 271.230 -524.460 14.926 2.113967e-04
35 0.732 1.924 NA 0.111 NA NA NA -0.003 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.304 -0.231 0.023 8 270.143 -524.287 15.099 1.938857e-04
41 0.795 1.932 NA NA NA -0.045 NA -0.009 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.276 -0.247 0.021 8 270.044 -524.087 15.298 1.754666e-04
38 0.711 1.934 + NA -0.076 NA NA -0.002 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.285 -0.241 0.016 9 270.938 -523.877 15.509 1.579452e-04
36 0.681 1.924 + 0.119 NA NA NA 0.001 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.314 -0.240 0.026 9 270.881 -523.762 15.623 1.491344e-04
524329 0.796 1.934 NA NA NA -0.044 NA 0.011 NA NA NA NA NA NA NA NA NA NA NA NA NA -0.025 NA 0.277 -0.243 0.025 9 270.806 -523.612 15.773 1.383564e-04
32805 0.743 1.933 NA NA -0.077 NA NA -0.004 NA NA NA NA NA NA NA NA NA 0.01 NA NA NA NA NA 0.280 -0.237 0.014 9 270.625 -523.250 16.136 1.154403e-04
266 0.775 1.932 + NA NA -0.059 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA 0.283 -0.251 0.024 9 270.603 -523.207 16.178 1.129936e-04
42 0.759 1.932 + NA NA -0.045 NA -0.007 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.281 -0.253 0.023 9 270.461 -522.922 16.463 9.798875e-05
1 0.760 1.928 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.275 -0.235 0.017 6 267.401 -522.802 16.584 9.227197e-05
8227 0.733 1.924 NA 0.110 NA NA NA -0.007 NA NA NA NA NA NA NA 0.021 NA NA NA NA NA NA NA 0.303 -0.231 0.023 9 270.255 -522.511 16.875 7.977602e-05
2 0.724 1.929 + NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.281 -0.241 0.018 7 267.796 -521.591 17.794 5.037447e-05
33 0.759 1.928 NA NA NA NA NA -0.014 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.275 -0.234 0.015 7 267.426 -520.853 18.533 3.482380e-05
34 0.724 1.929 + NA NA NA NA -0.012 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.280 -0.240 0.016 8 267.814 -519.628 19.758 1.887277e-05
1058 0.725 1.930 + NA NA NA NA -0.041 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA 0.286 -0.243 0.015 9 268.079 -518.159 21.227 9.054444e-06

Felidae

Code
TC_global_F <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label),
                      dispformula = ~p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf_F, 
                   family=beta_family(), REML = F,
                   na.action = "na.fail")

TC_selec_F <- dredge(TC_global_F, rank = "AIC", 
                   fixed = c("disp(p_distance)","disp(Lat_abs)","disp(Samp_dur)"), 
                   m.lim= c(NA,6))
Code
kbl(TC_selec_F, caption = "Fixed-effects structure selection table for temporal co-occurrence data when Felidae is dominant competitor", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Fixed-effects structure selection table for temporal co-occurrence data when Felidae is dominant competitor
cond((Int)) disp((Int)) cond(diet_dist) cond(Lat_abs) cond(mass_ratio) cond(I(mass_ratio^2)) cond(p_distance) cond(Samp_dur) cond(diet_dist:Lat_abs) cond(diet_dist:mass_ratio) cond(diet_dist:I(mass_ratio^2)) cond(diet_dist:p_distance) cond(diet_dist:Samp_dur) cond(Lat_abs:mass_ratio) cond(Lat_abs:p_distance) cond(Lat_abs:Samp_dur) cond(mass_ratio:p_distance) cond(mass_ratio:Samp_dur) cond(I(mass_ratio^2):Lat_abs) cond(I(mass_ratio^2):mass_ratio) cond(I(mass_ratio^2):p_distance) cond(I(mass_ratio^2):Samp_dur) cond(p_distance:Samp_dur) disp(Lat_abs) disp(p_distance) disp(Samp_dur) df logLik AIC delta weight
530 0.598 2.215 + NA NA NA 0.275 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA 0.408 -0.335 0.011 9 172.529 -327.058 0.000 6.881908e-01
18 0.883 2.194 + NA NA NA -0.211 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.401 -0.350 0.014 8 169.317 -322.635 4.423 7.538586e-02
262169 0.672 2.180 NA NA NA -0.041 -0.195 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.09 NA NA 0.407 -0.395 -0.011 9 170.178 -322.356 4.702 6.557553e-02
20 0.882 2.195 + 0.087 NA NA -0.217 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.421 -0.351 0.019 9 170.072 -322.143 4.914 5.897087e-02
26 0.890 2.188 + NA NA -0.016 -0.205 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.393 -0.352 0.014 9 169.567 -321.135 5.923 3.560951e-02
22 0.884 2.197 + NA 0.019 NA -0.214 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.404 -0.351 0.014 9 169.419 -320.838 6.220 3.069623e-02
50 0.881 2.193 + NA NA NA -0.211 0.020 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.404 -0.351 0.015 9 169.357 -320.714 6.344 2.885067e-02
17 0.643 2.154 NA NA NA NA -0.148 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.413 -0.374 0.009 7 164.997 -315.993 11.064 2.723283e-03
19 0.641 2.156 NA 0.080 NA NA -0.154 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.431 -0.375 0.015 8 165.645 -315.290 11.768 1.915790e-03
25 0.663 2.149 NA NA NA -0.022 -0.142 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.401 -0.377 0.010 8 165.498 -314.996 12.062 1.654126e-03
29 0.687 2.153 NA NA 0.072 -0.047 -0.151 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.394 -0.382 0.012 9 166.405 -314.811 12.247 1.507832e-03
4115 0.631 2.155 NA 0.095 NA NA -0.152 NA NA NA NA NA NA NA 0.05 NA NA NA NA NA NA NA NA 0.439 -0.388 0.013 9 166.261 -314.522 12.536 1.304804e-03
49 0.643 2.154 NA NA NA NA -0.150 0.035 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.417 -0.377 0.013 8 165.122 -314.244 12.814 1.135595e-03
21 0.644 2.157 NA NA 0.018 NA -0.152 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.415 -0.375 0.009 8 165.088 -314.177 12.881 1.098302e-03
27 0.659 2.151 NA 0.074 NA -0.020 -0.148 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.419 -0.378 0.016 9 166.056 -314.111 12.946 1.062755e-03
23 0.641 2.159 NA 0.082 0.022 NA -0.159 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.434 -0.376 0.015 9 165.777 -313.554 13.503 8.045192e-04
51 0.640 2.155 NA 0.079 NA NA -0.156 0.033 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.434 -0.378 0.018 9 165.761 -313.522 13.536 7.914406e-04
57 0.663 2.148 NA NA NA -0.022 -0.144 0.034 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.405 -0.380 0.014 9 165.621 -313.241 13.816 6.880031e-04
16405 0.636 2.165 NA NA 0.022 NA -0.151 NA NA NA NA NA NA NA NA NA 0.033 NA NA NA NA NA NA 0.429 -0.374 0.007 9 165.369 -312.739 14.319 5.350216e-04
1048625 0.646 2.155 NA NA NA NA -0.149 0.022 NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.02 0.421 -0.381 0.014 9 165.271 -312.542 14.515 4.850039e-04
53 0.643 2.156 NA NA 0.018 NA -0.153 0.035 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.419 -0.377 0.013 9 165.210 -312.421 14.637 4.564069e-04
131085 0.852 2.168 NA NA -0.014 -0.201 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.06 NA NA NA 0.386 -0.349 0.008 9 164.500 -311.000 16.058 2.242687e-04
65547 0.754 2.167 NA -0.015 NA -0.025 NA NA NA NA NA NA NA NA NA NA NA NA 0.079 NA NA NA NA 0.394 -0.305 0.008 9 163.969 -309.937 17.120 1.318400e-04
134 0.915 2.184 + NA -0.170 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA 0.359 -0.255 0.013 9 162.028 -306.057 21.001 1.894205e-05
9 0.746 2.144 NA NA NA -0.032 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.379 -0.306 0.014 7 160.016 -306.031 21.026 1.870468e-05
1 0.721 2.153 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.394 -0.294 0.012 6 158.971 -305.942 21.115 1.789021e-05
2 0.808 2.166 + NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.386 -0.273 0.013 7 159.539 -305.078 21.980 1.160931e-05
10 0.827 2.157 + NA NA -0.031 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.372 -0.286 0.013 8 160.511 -305.021 22.036 1.128793e-05
13 0.764 2.148 NA NA 0.045 -0.048 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.375 -0.306 0.015 8 160.372 -304.744 22.314 9.825315e-06
3 0.722 2.154 NA 0.047 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.402 -0.293 0.015 7 159.193 -304.387 22.671 8.219223e-06
11 0.746 2.145 NA 0.040 NA -0.031 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.387 -0.305 0.016 8 160.181 -304.363 22.695 8.120696e-06
524329 0.749 2.156 NA NA NA -0.036 NA 0.038 NA NA NA NA NA NA NA NA NA NA NA NA NA -0.037 NA 0.390 -0.298 0.021 9 161.173 -304.346 22.711 8.053983e-06
41 0.746 2.144 NA NA NA -0.032 NA 0.016 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.381 -0.307 0.015 8 160.043 -304.086 22.971 7.072244e-06
5 0.719 2.151 NA NA -0.011 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.393 -0.296 0.012 7 159.007 -304.015 23.043 6.824599e-06
33 0.721 2.153 NA NA NA NA NA 0.016 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.396 -0.295 0.014 7 158.997 -303.994 23.064 6.751910e-06
14 0.835 2.159 + NA 0.039 -0.044 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.369 -0.288 0.014 9 160.772 -303.545 23.513 5.394352e-06
4 0.807 2.167 + 0.045 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.393 -0.272 0.015 8 159.739 -303.477 23.581 5.215137e-06
12 0.826 2.157 + 0.039 NA -0.030 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.379 -0.285 0.016 9 160.660 -303.321 23.737 4.823013e-06
266 0.851 2.159 + NA NA -0.047 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA 0.373 -0.282 0.014 9 160.603 -303.207 23.851 4.556173e-06
6 0.808 2.164 + NA -0.014 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.384 -0.274 0.012 8 159.598 -303.196 23.862 4.530881e-06
34 0.808 2.166 + NA NA NA NA 0.008 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.387 -0.273 0.013 8 159.545 -303.090 23.967 4.297917e-06
15 0.765 2.149 NA 0.041 0.045 -0.047 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.383 -0.305 0.017 9 160.540 -303.081 23.977 4.277549e-06
42 0.826 2.157 + NA NA -0.031 NA 0.009 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.373 -0.287 0.014 9 160.519 -303.038 24.020 4.186650e-06
45 0.764 2.148 NA NA 0.045 -0.047 NA 0.014 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.376 -0.307 0.016 9 160.392 -302.785 24.273 3.689215e-06
7 0.720 2.152 NA 0.046 -0.010 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.401 -0.294 0.015 8 159.222 -302.445 24.613 3.112129e-06
35 0.722 2.153 NA 0.046 NA NA NA 0.014 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.404 -0.294 0.017 8 159.214 -302.429 24.629 3.087942e-06
43 0.747 2.145 NA 0.040 NA -0.031 NA 0.015 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.388 -0.306 0.018 9 160.205 -302.410 24.648 3.058583e-06
37 0.720 2.151 NA NA -0.012 NA NA 0.017 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.395 -0.296 0.014 8 159.035 -302.070 24.987 2.580925e-06
1058 0.822 2.168 + NA NA NA NA -0.056 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA 0.390 -0.274 0.012 9 160.000 -302.000 25.058 2.491836e-06
8 0.808 2.165 + 0.044 -0.013 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.392 -0.273 0.015 9 159.788 -301.577 25.481 2.016452e-06
68 0.806 2.166 + 0.059 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.393 -0.272 0.015 9 159.754 -301.508 25.549 1.948868e-06
36 0.807 2.167 + 0.045 NA NA NA 0.007 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.394 -0.272 0.016 9 159.743 -301.486 25.572 1.926852e-06
38 0.808 2.164 + NA -0.014 NA NA 0.009 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.385 -0.274 0.013 9 159.605 -301.210 25.847 1.679022e-06
8227 0.718 2.152 NA 0.033 NA NA NA 0.012 NA NA NA NA NA NA NA 0.051 NA NA NA NA NA NA NA 0.398 -0.293 0.013 9 159.582 -301.163 25.894 1.639933e-06
2055 0.723 2.156 NA 0.056 -0.004 NA NA NA NA NA NA NA NA 0.041 NA NA NA NA NA NA NA NA NA 0.400 -0.283 0.018 9 159.558 -301.116 25.942 1.601565e-06
39 0.720 2.152 NA 0.045 -0.010 NA NA 0.015 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.403 -0.295 0.017 9 159.245 -300.490 26.567 1.171307e-06
32805 0.720 2.151 NA NA -0.011 NA NA 0.016 NA NA NA NA NA NA NA NA NA -0.01 NA NA NA NA NA 0.393 -0.295 0.012 9 159.070 -300.139 26.918 9.827321e-07

Canidae

Code
TC_global_C <- glmmTMB(formula = Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2+ (1|Label),
                      dispformula = ~Samp_dur+Lat_abs,
                   data=tempC_modsdf_C, 
                   family=beta_family(), REML = F,
                   na.action = "na.fail")

TC_selec_C <- dredge(TC_global_C, rank = "AIC", 
                   fixed = c("disp(Lat_abs)","disp(Samp_dur)"), 
                   m.lim= c(NA,5))
Code
kbl(TC_selec_C, caption = "Fixed-effects structure selection table for temporal co-occurrence data when Canidae is dominant competitor", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Fixed-effects structure selection table for temporal co-occurrence data when Canidae is dominant competitor
cond((Int)) disp((Int)) cond(diet_dist) cond(Lat_abs) cond(mass_ratio) cond(I(mass_ratio^2)) cond(p_distance) cond(Samp_dur) cond(diet_dist:Lat_abs) cond(diet_dist:mass_ratio) cond(diet_dist:I(mass_ratio^2)) cond(diet_dist:p_distance) cond(diet_dist:Samp_dur) cond(Lat_abs:mass_ratio) cond(Lat_abs:p_distance) cond(Lat_abs:Samp_dur) cond(mass_ratio:p_distance) cond(mass_ratio:Samp_dur) cond(I(mass_ratio^2):Lat_abs) cond(I(mass_ratio^2):mass_ratio) cond(I(mass_ratio^2):p_distance) cond(I(mass_ratio^2):Samp_dur) cond(p_distance:Samp_dur) disp(Lat_abs) disp(Samp_dur) df logLik AIC delta weight
7 0.375 1.860 NA 0.389 -0.414 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.700 0.006 7 66.190 -118.380 0.000 2.894945e-01
39 0.399 1.889 NA 0.381 -0.411 NA NA 0.116 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.662 0.047 8 66.848 -117.696 0.684 2.056270e-01
2055 0.294 1.826 NA 0.457 -0.530 NA NA NA NA NA NA NA NA 0.114 NA NA NA NA NA NA NA NA NA 0.735 -0.015 8 66.585 -117.170 1.210 1.580876e-01
23 0.349 1.865 NA 0.394 -0.420 NA 0.036 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.697 0.003 8 66.248 -116.496 1.885 1.128123e-01
15 0.382 1.858 NA 0.389 -0.423 -0.022 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.701 0.001 8 66.207 -116.413 1.967 1.082773e-01
8 0.370 1.859 + 0.389 -0.414 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.703 0.007 8 66.195 -116.389 1.991 1.069721e-01
16405 0.933 2.027 NA NA 0.019 NA -0.274 NA NA NA NA NA NA NA NA NA -0.583 NA NA NA NA NA NA 0.581 0.102 8 62.507 -109.014 9.366 2.677861e-03
68 0.716 1.692 + 0.195 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.856 0.301 8 62.386 -108.771 9.609 2.371765e-03
32805 0.727 2.049 NA NA -0.400 NA NA 0.184 NA NA NA NA NA NA NA NA NA 0.154 NA NA NA NA NA 0.507 0.109 8 62.324 -108.648 9.732 2.229997e-03
5 0.721 1.998 NA NA -0.372 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.537 0.085 6 60.287 -108.574 9.807 2.148439e-03
37 0.738 2.006 NA NA -0.370 NA NA 0.119 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.523 0.104 7 60.780 -107.559 10.821 1.293790e-03
6 0.709 1.997 + NA -0.371 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.544 0.088 7 60.308 -106.615 11.765 8.069527e-04
13 0.727 1.998 NA NA -0.379 -0.019 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.536 0.082 7 60.298 -106.596 11.784 7.992806e-04
21 0.723 1.997 NA NA -0.372 NA -0.004 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.538 0.085 7 60.287 -106.575 11.806 7.907651e-04
131085 0.755 2.018 NA NA -0.088 -0.064 NA NA NA NA NA NA NA NA NA NA NA NA NA -0.262 NA NA NA 0.521 0.127 8 61.000 -105.999 12.381 5.930561e-04
38 0.721 2.006 + NA -0.369 NA NA 0.122 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.531 0.109 8 60.819 -105.638 12.742 4.950643e-04
45 0.746 2.007 NA NA -0.380 -0.025 NA 0.121 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.521 0.100 8 60.800 -105.599 12.781 4.855250e-04
53 0.741 2.005 NA NA -0.369 NA -0.006 0.119 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.523 0.104 8 60.781 -105.562 12.819 4.765406e-04
11 0.485 1.792 NA 0.326 NA 0.205 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.634 0.139 7 59.567 -105.135 13.246 3.849030e-04
134 0.725 1.995 + NA -0.321 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA 0.551 0.096 8 60.388 -104.777 13.604 3.218573e-04
8227 0.529 1.746 NA 0.381 NA NA NA 0.198 NA NA NA NA NA NA NA -0.111 NA NA NA NA NA NA NA 0.635 0.195 8 60.354 -104.709 13.671 3.111162e-04
14 0.715 1.998 + NA -0.378 -0.019 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.542 0.085 8 60.319 -104.639 13.742 3.004070e-04
22 0.710 1.997 + NA -0.371 NA -0.002 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.544 0.088 8 60.308 -104.615 13.765 2.969139e-04
43 0.501 1.815 NA 0.322 NA 0.197 NA 0.119 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.600 0.174 8 60.301 -104.602 13.778 2.949221e-04
29 0.728 1.998 NA NA -0.379 -0.019 -0.002 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.536 0.082 8 60.298 -104.596 13.784 2.940799e-04
3 0.595 1.773 NA 0.318 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.623 0.111 6 58.044 -104.087 14.293 2.279989e-04
35 0.608 1.796 NA 0.315 NA NA NA 0.129 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.588 0.151 7 58.876 -103.752 14.628 1.928109e-04
27 0.504 1.789 NA 0.323 NA 0.205 -0.032 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.636 0.137 8 59.608 -103.215 15.165 1.474204e-04
12 0.471 1.792 + 0.327 NA 0.204 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.642 0.144 8 59.592 -103.184 15.197 1.451133e-04
65547 0.480 1.792 NA 0.332 NA 0.210 NA NA NA NA NA NA NA NA NA NA NA NA -0.008 NA NA NA NA 0.632 0.136 8 59.569 -103.139 15.241 1.419051e-04
19 0.613 1.770 NA 0.315 NA NA -0.028 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.624 0.109 7 58.075 -102.150 16.231 8.653516e-05
4 0.580 1.773 + 0.319 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.631 0.117 7 58.071 -102.142 16.238 8.620106e-05
36 0.587 1.796 + 0.315 NA NA NA 0.132 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.599 0.161 8 58.931 -101.862 16.518 7.495955e-05
51 0.627 1.793 NA 0.311 NA NA -0.029 0.128 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.589 0.150 8 58.909 -101.819 16.562 7.332957e-05
20 0.598 1.770 + 0.316 NA NA -0.025 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.631 0.115 8 58.096 -100.192 18.188 3.251744e-05
4115 0.578 1.776 NA 0.341 NA NA 0.019 NA NA NA NA NA NA NA -0.036 NA NA NA NA NA NA NA NA 0.618 0.109 8 58.092 -100.184 18.197 3.238218e-05
1058 0.897 1.872 + NA NA NA NA 0.048 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA 0.632 0.324 8 57.830 -99.660 18.720 2.492425e-05
9 0.770 1.910 NA NA NA 0.179 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.481 0.185 6 55.199 -98.399 19.982 1.326319e-05
1 0.860 1.897 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.466 0.163 5 54.052 -98.104 20.276 1.144961e-05
41 0.784 1.916 NA NA NA 0.174 NA 0.115 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.466 0.201 7 55.715 -97.430 20.951 8.170185e-06
33 0.872 1.903 NA NA NA NA NA 0.124 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.451 0.183 6 54.640 -97.279 21.101 7.578664e-06
25 0.806 1.905 NA NA NA 0.181 -0.065 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.483 0.183 7 55.349 -96.699 21.682 5.668781e-06
10 0.753 1.910 + NA NA 0.179 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.491 0.192 7 55.239 -96.478 21.902 5.077442e-06
17 0.895 1.892 NA NA NA NA -0.061 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.467 0.160 6 54.181 -96.362 22.018 4.790789e-06
2 0.841 1.896 + NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.476 0.171 6 54.098 -96.196 22.185 4.408217e-06
57 0.821 1.911 NA NA NA 0.175 -0.068 0.115 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.468 0.200 8 55.878 -95.756 22.624 3.539371e-06
524329 0.790 1.907 NA NA NA 0.163 NA 0.085 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.049 NA 0.490 0.207 8 55.832 -95.664 22.716 3.380105e-06
49 0.908 1.898 NA NA NA NA -0.064 0.124 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.451 0.181 7 54.783 -95.566 22.814 3.218172e-06
42 0.761 1.915 + NA NA 0.173 NA 0.119 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.479 0.211 8 55.783 -95.565 22.815 3.216761e-06
262169 0.873 1.909 NA NA NA 0.021 -0.165 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.244 NA NA 0.482 0.194 8 55.735 -95.470 22.911 3.066770e-06
34 0.848 1.902 + NA NA NA NA 0.128 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.464 0.193 7 54.716 -95.431 22.949 3.008018e-06
266 0.699 1.919 + NA NA 0.283 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA 0.480 0.173 8 55.597 -95.194 23.186 2.672203e-06
26 0.790 1.904 + NA NA 0.181 -0.062 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.492 0.189 8 55.375 -94.750 23.630 2.140035e-06
18 0.877 1.892 + NA NA NA -0.057 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.476 0.167 7 54.211 -94.421 23.959 1.815577e-06
1048625 0.901 1.900 NA NA NA NA -0.052 0.073 NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.081 0.455 0.186 8 54.919 -93.838 24.543 1.355947e-06
50 0.884 1.898 + NA NA NA -0.059 0.128 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.463 0.190 8 54.837 -93.674 24.706 1.249672e-06
530 0.850 1.887 + NA NA NA -0.013 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA 0.481 0.166 8 54.358 -92.715 25.665 7.736914e-07

Mustealidae

Code
tempC_modsdf_M2 <- slice(tempC_modsdf_M, -27)

TC_global_M <- betareg(Ov_coeff ~ (mass_ratio+ I(mass_ratio^2)+p_distance + diet_dist+Lat_abs+Samp_dur)^2,
                         data=tempC_modsdf_M2, 
                         na.action = "na.fail")

TC_selec_M <- dredge(TC_global_M, rank = "AIC", 
                   m.lim= c(NA,3))
Code
kbl(TC_selec_M, caption = "Fixed-effects structure selection table for temporal co-occurrence data when Mustelidae is dominant competitor", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F)
Fixed-effects structure selection table for temporal co-occurrence data when Mustelidae is dominant competitor
(Intercept) diet_dist Lat_abs mass_ratio I(mass_ratio^2) p_distance Samp_dur diet_dist:Lat_abs diet_dist:mass_ratio diet_dist:I(mass_ratio^2) diet_dist:p_distance diet_dist:Samp_dur Lat_abs:mass_ratio Lat_abs:p_distance Lat_abs:Samp_dur mass_ratio:p_distance mass_ratio:Samp_dur I(mass_ratio^2):Lat_abs I(mass_ratio^2):mass_ratio I(mass_ratio^2):p_distance I(mass_ratio^2):Samp_dur p_distance:Samp_dur df logLik AIC delta weight
20 -0.051 + 0.387 NA NA 0.392 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 44.905 -79.811 0.000 7.762372e-01
42 0.550 + NA NA -0.196 NA -0.368 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 42.156 -74.312 5.499 4.964749e-02
12 0.463 + 0.228 NA -0.187 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 42.028 -74.056 5.755 4.368093e-02
26 0.510 + NA NA -0.180 0.212 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 41.365 -72.731 7.080 2.251960e-02
50 0.213 + NA NA NA 0.244 -0.367 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 40.879 -71.759 8.052 1.385403e-02
8 0.213 + 0.256 -0.170 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 40.568 -71.135 8.676 1.014190e-02
266 0.690 + NA NA -0.240 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA 5 40.443 -70.886 8.925 8.954648e-03
10 0.651 + NA NA -0.205 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 39.386 -70.772 9.039 8.457681e-03
38 0.310 + NA -0.156 NA NA -0.367 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 39.992 -69.984 9.827 5.703549e-03
14 0.601 + NA -0.090 -0.175 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 39.905 -69.810 10.001 5.228230e-03
27 0.512 NA 0.313 NA -0.197 0.160 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 39.904 -69.807 10.004 5.221000e-03
11 0.625 NA 0.249 NA -0.216 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 38.711 -69.423 10.388 4.308490e-03
43 0.619 NA 0.177 NA -0.215 NA -0.249 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 39.704 -69.408 10.403 4.276712e-03
36 0.243 + 0.177 NA NA NA -0.257 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 39.603 -69.206 10.605 3.865914e-03
530 0.204 + NA NA NA 0.435 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA 5 39.551 -69.102 10.708 3.670657e-03
4 0.250 + 0.252 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 38.497 -68.994 10.817 3.476237e-03
41 0.739 NA NA NA -0.228 NA -0.376 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 38.444 -68.889 10.922 3.298852e-03
34 0.341 + NA NA NA NA -0.385 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 38.311 -68.622 11.189 2.886762e-03
18 0.297 + NA NA NA 0.258 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 38.178 -68.357 11.454 2.528047e-03
68 0.198 + 0.325 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 39.071 -68.141 11.669 2.270187e-03
15 0.598 NA 0.254 -0.058 -0.198 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 38.934 -67.867 11.943 1.979477e-03
65547 0.589 NA 0.329 NA -0.178 NA NA NA NA NA NA NA NA NA NA NA NA -0.099 NA NA NA NA 5 38.930 -67.860 11.951 1.971698e-03
22 0.303 + NA -0.105 NA 0.209 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 38.856 -67.711 12.099 1.830980e-03
134 0.387 + NA -0.256 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA NA NA NA 5 38.724 -67.449 12.362 1.605798e-03
524329 0.739 NA NA NA -0.225 NA -0.451 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.102 NA 5 38.635 -67.270 12.541 1.468064e-03
1058 0.325 + NA NA NA NA -0.456 NA NA NA NA + NA NA NA NA NA NA NA NA NA NA 5 38.595 -67.190 12.620 1.411026e-03
57 0.724 NA NA NA -0.225 0.045 -0.374 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 38.552 -67.104 12.707 1.351306e-03
45 0.727 NA NA -0.031 -0.219 NA -0.373 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 38.509 -67.019 12.792 1.295074e-03
4115 0.073 NA 0.540 NA NA 0.488 NA NA NA NA NA NA NA -0.322 NA NA NA NA NA NA NA NA 5 38.386 -66.773 13.038 1.145086e-03
6 0.400 + NA -0.171 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 37.341 -66.681 13.129 1.093953e-03
9 0.847 NA NA NA -0.239 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 35.814 -65.628 14.183 6.460790e-04
131085 0.747 NA NA 0.212 -0.054 NA NA NA NA NA NA NA NA NA NA NA NA NA -0.144 NA NA NA 5 37.485 -64.969 14.841 4.647566e-04
2 0.436 + NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 35.422 -64.843 14.967 4.363696e-04
8227 0.458 NA 0.275 NA NA NA -0.350 NA NA NA NA NA NA NA 0.343 NA NA NA NA NA NA NA 5 37.365 -64.730 15.081 4.123065e-04
19 0.281 NA 0.365 NA NA 0.207 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 36.186 -64.372 15.438 3.448571e-04
25 0.829 NA NA NA -0.235 0.051 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 35.948 -63.896 15.914 2.717865e-04
13 0.830 NA NA -0.042 -0.227 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 35.924 -63.847 15.963 2.651965e-04
51 0.293 NA 0.302 NA NA 0.182 -0.179 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 36.669 -63.338 16.473 2.055938e-04
2055 0.341 NA 0.343 -0.265 NA NA NA NA NA NA NA NA 0.184 NA NA NA NA NA NA NA NA NA 5 36.656 -63.312 16.499 2.029507e-04
23 0.289 NA 0.357 -0.090 NA 0.168 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 36.648 -63.297 16.514 2.013886e-04
7 0.379 NA 0.292 -0.141 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 35.605 -63.209 16.601 1.927815e-04
39 0.375 NA 0.226 -0.131 NA NA -0.225 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 36.391 -62.782 17.028 1.557298e-04
3 0.403 NA 0.281 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 34.335 -62.670 17.141 1.472128e-04
35 0.398 NA 0.208 NA NA NA -0.251 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 35.302 -62.605 17.206 1.424715e-04
262169 0.830 NA NA NA -0.227 -0.030 NA NA NA NA NA NA NA NA NA NA NA NA NA 0.087 NA NA 5 36.106 -62.212 17.599 1.170713e-04
29 0.822 NA NA -0.028 -0.228 0.039 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 35.990 -61.981 17.830 1.042925e-04
33 0.525 NA NA NA NA NA -0.401 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 33.655 -61.310 18.501 7.458279e-05
37 0.513 NA NA -0.115 NA NA -0.387 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 34.454 -60.908 18.903 6.099542e-05
32805 0.514 NA NA -0.059 NA NA -0.361 NA NA NA NA NA NA NA NA NA 0.268 NA NA NA NA NA 5 35.442 -60.884 18.926 6.027970e-05
49 0.506 NA NA NA NA 0.068 -0.397 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 33.883 -59.765 20.046 3.444807e-05
53 0.508 NA NA -0.107 NA 0.022 -0.387 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 34.473 -58.947 20.864 2.288102e-05
1048625 0.521 NA NA NA NA -0.001 -0.354 NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.21 5 34.280 -58.559 21.252 1.884820e-05
1 0.628 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 2 30.844 -57.687 22.123 1.218964e-05
5 0.612 NA NA -0.131 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 31.842 -57.684 22.127 1.216686e-05
17 0.606 NA NA NA NA 0.077 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 31.119 -56.239 23.572 5.907693e-06
21 0.606 NA NA -0.123 NA 0.024 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 4 31.864 -55.729 24.082 4.577766e-06
16405 0.611 NA NA -0.120 NA 0.048 NA NA NA NA NA NA NA NA NA 0.036 NA NA NA NA NA NA 5 31.887 -53.774 26.037 1.722455e-06

Confidence intervals explorations

Code
# Function to get 85%IC
get_cibeta <- function(mod_name, mods){
  ci_df <- parameters::model_parameters(mods, ci = 0.85) %>% 
    select(Parameter, Coefficient, CI_low, CI_high) %>% 
    filter(Parameter != "(Intercept)") %>%
    mutate(Model = mod_name,
           Informative = case_when(
    CI_low < 0 & CI_high < 0 ~ "yes",
    CI_low > 0 & CI_high > 0 ~ "yes",
    TRUE ~ "no")) 
  return(ci_df)   
}

Consistent with the model selection strategy (AIC) and to avoid uninformative variables, we explored the 85% confidence intervals of the regression coefficients of the best models (Sutherland et al. 2023). Variables whose 85% CI overlap 0 are considered as uninformative and therefore not included in the inference (Arnold 2010).

Code
# get best models for all data 
TC_best_mods <- get.models(TC_selec, subset = delta <2, REML = T)
# get best models for felidae subset data
TC_best_mods_F <- get.models(TC_selec_F, subset = delta <2, REML = T)
# get best models for Canidae subset data
TC_best_mods_C <- get.models(TC_selec_C, subset = delta <2, REML = T)
# get best models for Mustelidae subset data
TC_best_mods_M <- get.models(TC_selec_M, subset = delta <2)

# Apply the function to obtain the table of coefficients of selected the models
TC_best_ci <- map2_df(names(TC_best_mods), TC_best_mods, get_ci) 
TC_best_ci_F <- map2_df(names(TC_best_mods_F), TC_best_mods_F, get_ci)
TC_best_ci_C <- map2_df(names(TC_best_mods_C), TC_best_mods_C, get_ci)
TC_best_ci_M <- map2_df(names(TC_best_mods_M), TC_best_mods_M, get_cibeta) 

ci_plot(TC_best_ci)+ labs(title= "All data")
ci_plot(TC_best_ci_F)+ labs(title= "Felidae dominant competitor")
ci_plot(TC_best_ci_C)+ labs(title= "Canidae dominant competitor")
ci_plot(TC_best_ci_M)+ labs(title= "Mustelidae dominant competitor")

All data best model 85% CI

Felidae data best model 85% CI

Canidae data best model 85% CI

Mustelidae data best model 85% CI

Summary selected models

Note that some variables have coefficients whose 85% confidence intervals overlap 0. These variables are retained when they have interactions with other variables and these interactions do not overlap with 0.

Spatial co-occurrence models

Code
SC_mod1 <- glmmTMB(formula = SIF~ I(mass_ratio^2)+ p_distance,
                   data=spatC_modsdf,                     
                   family= t_family(link = "identity"),
                   REML = F,                    
                   start = list(psi = log(1.69)),
                   map = list(psi = factor(NA))) 

SC_mod2 <- glmmTMB(formula = SIF~ I(mass_ratio^2),
                   data=spatC_modsdf,                     
                   family= t_family(link = "identity"),
                   REML = F,                    
                   start = list(psi = log(1.69)), 
                   map = list(psi = factor(NA)))  


SC_mods <- list(SC_mod1, SC_mod2) %>%    
  map(model_parameters, digits= 2, ci= 0.85) %>%    
  reduce(rbind) %>%   
  mutate(Model= c(rep("SIF~ I(mass_ratio^2)+ p_distance", 4),
                  rep("SIF~ I(mass_ratio^2)", 3))) %>%    
  select(-SE, -z, -df_error)    
Code
SC_mod1_F <- glmmTMB(formula = SIF~ I(mass_ratio^2)*Lat_abs,
                     dispformula = ~ mass_ratio+p_distance+Lat_abs+ Avg_dist,
                     data=spatC_modsdf_F,
                     family=t_family(link = "identity"),
                     REML = F,
                     start = list(psi = log(2.87)),
                     map = list(psi = factor(NA)))   

SC_mod2_F <- glmmTMB(formula = SIF~ I(mass_ratio^2)+ Lat_abs,
                     dispformula = ~ mass_ratio+p_distance+Lat_abs+ Avg_dist,
                     data=spatC_modsdf_F,
                     family=t_family(link = "identity"),
                     REML = F,
                     start = list(psi = log(2.87)),
                     map = list(psi = factor(NA)))  

SC_mod3_F <- glmmTMB(formula = SIF~ I(mass_ratio^2),
                     dispformula = ~ mass_ratio+p_distance+Lat_abs+ Avg_dist,
                     data=spatC_modsdf_F,
                     family=t_family(link = "identity"),
                     REML = F,
                     start = list(psi = log(2.87)),
                     map = list(psi = factor(NA)))

SC_mod4_F <- glmmTMB(formula = SIF~ I(mass_ratio^2)*p_distance,
                     dispformula = ~ mass_ratio+p_distance+Lat_abs+ Avg_dist,
                     data=spatC_modsdf_F,
                     family=t_family(link = "identity"),                    
                     REML = F,
                     start = list(psi = log(2.87)),           
                     map = list(psi = factor(NA)))  

SC_mods_F <- list(SC_mod1_F, SC_mod2_F, SC_mod3_F, SC_mod4_F) %>%
  map(model_parameters, digits= 2, ci= 0.85) %>%
  reduce(rbind) %>%   
  mutate(Model= c(rep("SIF~ I(mass_ratio^2)* Lat_abs", 9),
                  rep("SIF~ I(mass_ratio^2)+ Lat_abs", 8),
                  rep("SIF~ I(mass_ratio^2)", 7),
                  rep("SIF~ I(mass_ratio^2)*p_distance", 9))) %>%
  select(-SE, -z, -df_error)
Code
SC_mods_tab <- rbind(SC_mods, SC_mods_F)

kbl(SC_mods_tab, 
    caption = "Spatial co-occurrence selected models", digits = 3) %>%
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F) %>% 
    pack_rows("Spatial co-occurrence models -all data",1, nrow(SC_mods)) %>%
  pack_rows("Spatial co-occurrence models -Felidae as dominant competitor",1 + nrow(SC_mods),nrow(SC_mods)+ nrow(SC_mods_F))
Spatial co-occurrence selected models
Parameter Coefficient CI CI_low CI_high p Component Effects Model
Spatial co-occurrence models -all data
(Intercept) 1.032 0.85 1.002 1.062 0.000 conditional fixed SIF~ I(mass_ratio^2)+ p_distance
I(mass_ratio^2) -0.024 0.85 -0.040 -0.007 0.036 conditional fixed SIF~ I(mass_ratio^2)+ p_distance
p_distance 0.028 0.85 0.003 0.052 0.102 conditional fixed SIF~ I(mass_ratio^2)+ p_distance
(Intercept) 0.180 0.85 0.152 0.212 NA dispersion fixed SIF~ I(mass_ratio^2)+ p_distance
(Intercept) 1.026 0.85 0.997 1.056 0.000 conditional fixed SIF~ I(mass_ratio^2)
I(mass_ratio^2) -0.021 0.85 -0.036 -0.005 0.056 conditional fixed SIF~ I(mass_ratio^2)
(Intercept) 0.182 0.85 0.154 0.215 NA dispersion fixed SIF~ I(mass_ratio^2)
Spatial co-occurrence models -Felidae as dominant competitor
(Intercept) 1.041 0.85 0.981 1.102 0.000 conditional fixed SIF~ I(mass_ratio^2)* Lat_abs
I(mass_ratio^2) -0.107 0.85 -0.176 -0.038 0.026 conditional fixed SIF~ I(mass_ratio^2)* Lat_abs
Lat_abs -0.001 0.85 -0.052 0.050 0.978 conditional fixed SIF~ I(mass_ratio^2)* Lat_abs
I(mass_ratio^2):Lat_abs -0.067 0.85 -0.128 -0.006 0.116 conditional fixed SIF~ I(mass_ratio^2)* Lat_abs
(Intercept) -1.609 0.85 -1.814 -1.405 0.000 dispersion fixed SIF~ I(mass_ratio^2)* Lat_abs
mass_ratio 0.024 0.85 -0.162 0.209 0.855 dispersion fixed SIF~ I(mass_ratio^2)* Lat_abs
p_distance -0.183 0.85 -0.394 0.029 0.214 dispersion fixed SIF~ I(mass_ratio^2)* Lat_abs
Lat_abs 0.109 0.85 -0.094 0.313 0.439 dispersion fixed SIF~ I(mass_ratio^2)* Lat_abs
Avg_dist -0.033 0.85 -0.342 0.276 0.878 dispersion fixed SIF~ I(mass_ratio^2)* Lat_abs
(Intercept) 0.995 0.85 0.946 1.045 0.000 conditional fixed SIF~ I(mass_ratio^2)+ Lat_abs
I(mass_ratio^2) -0.034 0.85 -0.053 -0.015 0.011 conditional fixed SIF~ I(mass_ratio^2)+ Lat_abs
Lat_abs -0.041 0.85 -0.080 -0.001 0.137 conditional fixed SIF~ I(mass_ratio^2)+ Lat_abs
(Intercept) -1.574 0.85 -1.779 -1.368 0.000 dispersion fixed SIF~ I(mass_ratio^2)+ Lat_abs
mass_ratio 0.025 0.85 -0.159 0.209 0.844 dispersion fixed SIF~ I(mass_ratio^2)+ Lat_abs
p_distance -0.138 0.85 -0.351 0.076 0.353 dispersion fixed SIF~ I(mass_ratio^2)+ Lat_abs
Lat_abs 0.147 0.85 -0.057 0.350 0.299 dispersion fixed SIF~ I(mass_ratio^2)+ Lat_abs
Avg_dist -0.036 0.85 -0.359 0.288 0.874 dispersion fixed SIF~ I(mass_ratio^2)+ Lat_abs
(Intercept) 1.018 0.85 0.976 1.061 0.000 conditional fixed SIF~ I(mass_ratio^2)
I(mass_ratio^2) -0.030 0.85 -0.049 -0.011 0.023 conditional fixed SIF~ I(mass_ratio^2)
(Intercept) -1.581 0.85 -1.790 -1.371 0.000 dispersion fixed SIF~ I(mass_ratio^2)
mass_ratio 0.018 0.85 -0.171 0.207 0.892 dispersion fixed SIF~ I(mass_ratio^2)
p_distance -0.086 0.85 -0.300 0.129 0.565 dispersion fixed SIF~ I(mass_ratio^2)
Lat_abs 0.127 0.85 -0.083 0.336 0.384 dispersion fixed SIF~ I(mass_ratio^2)
Avg_dist 0.038 0.85 -0.300 0.376 0.872 dispersion fixed SIF~ I(mass_ratio^2)
(Intercept) 1.011 0.85 0.971 1.052 0.000 conditional fixed SIF~ I(mass_ratio^2)*p_distance
I(mass_ratio^2) -0.016 0.85 -0.032 0.000 0.157 conditional fixed SIF~ I(mass_ratio^2)*p_distance
p_distance 0.024 0.85 -0.011 0.060 0.326 conditional fixed SIF~ I(mass_ratio^2)*p_distance
I(mass_ratio^2):p_distance -0.024 0.85 -0.041 -0.006 0.055 conditional fixed SIF~ I(mass_ratio^2)*p_distance
(Intercept) -1.613 0.85 -1.826 -1.399 0.000 dispersion fixed SIF~ I(mass_ratio^2)*p_distance
mass_ratio -0.053 0.85 -0.265 0.159 0.719 dispersion fixed SIF~ I(mass_ratio^2)*p_distance
p_distance -0.068 0.85 -0.282 0.146 0.648 dispersion fixed SIF~ I(mass_ratio^2)*p_distance
Lat_abs 0.125 0.85 -0.090 0.340 0.403 dispersion fixed SIF~ I(mass_ratio^2)*p_distance
Avg_dist 0.096 0.85 -0.261 0.454 0.698 dispersion fixed SIF~ I(mass_ratio^2)*p_distance

Goftest of spatial selected models

Code
SC_best_goft_list <- list(SC_mod1, SC_mod2) 
SC_best_goft <- lapply(SC_best_goft_list, simulateResiduals, plot=T)

SIF~ I(mass_ratio^2)+ p_distance goftest -all data

SIF~ I(mass_ratio^2) goftest - -all data

Code
SC_best_goft_list_F <- list(SC_mod1_F, SC_mod2_F, SC_mod3_F, SC_mod4_F) 
SC_best_goft_F <- lapply(SC_best_goft_list_F, simulateResiduals, plot=T)

SSIF~ I(mass_ratio^2)* Lat_abs goftest -Felidae as dominant competitor

SIF~ I(mass_ratio^2)+ Lat_abs goftest -Felidae as dominant competitor

SIF~ I(mass_ratio^2) goftest -Felidae as dominant competitor

SIF~ I(mass_ratio^2)*p_distance goftest -Felidae as dominant competitor

Because all models fit adequately, we base our inference on models that contain interactions of the variables

Temporal co-occurrence models

Code
TC_mod1 <- glmmTMB(formula = Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label),
                      dispformula = ~p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf, 
                   family=beta_family(), 
                   REML = T)


TC_mod2 <- glmmTMB(formula = Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label),
                      dispformula = ~p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf, 
                   family=beta_family(), 
                   REML = T)

TC_mod3 <- glmmTMB(formula = Ov_coeff ~ I(mass_ratio^2)*p_distance+  (1|Label),
                      dispformula = ~p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf, 
                   family=beta_family(), 
                   REML = T)

TC_mods <- list(TC_mod1, TC_mod2, TC_mod3) %>% 
  map(model_parameters, digits= 2, ci= 0.85) %>% 
  reduce(rbind) %>%
  mutate(Model= c(rep("Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)", 9),
                  rep(" Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)", 9),
                  rep("Ov_coeff ~ I(mass_ratio^2)*p_distance+  (1|Label)", 9))) %>% 
  select(-SE, -z, -df_error, -Group)
Code
TC_mod1_F <- glmmTMB(formula = Ov_coeff ~ p_distance*diet_dist+ (1|Label),
                      dispformula = ~p_distance+ Samp_dur+Lat_abs,
                   data=tempC_modsdf_F, 
                   family=beta_family(), 
                   REML = T)

TC_mods_F <- model_parameters(TC_mod1_F, digits= 2, ci= 0.85) %>% 
  mutate(Model= c(rep("Ov_coeff ~ p_distance*diet_dist+ (1|Label)", 9))) %>% 
  select(-SE, -z, -df_error, -Group)
Code
TC_mod1_C <- glmmTMB(formula = Ov_coeff ~ Lat_abs+ mass_ratio+ (1|Label),
                      dispformula = ~Samp_dur+Lat_abs,
                   data=tempC_modsdf_C, 
                   family=beta_family(), 
                   REML = T)

TC_mods_C <- list(TC_mod1_C) %>% 
  map(model_parameters, digits= 2, ci= 0.85) %>% 
  reduce(rbind) %>%
  mutate(Model= c(rep("Ov_coeff ~ Lat_abs+ mass_ratio+ (1|Label)", 7))) %>% 
  select(-SE, -z, -df_error,-Group)
Code
TC_mod1_M<- betareg(Ov_coeff ~ p_distance + diet_dist+Lat_abs,
                         data=tempC_modsdf_M2)

TC_mods_M <- model_parameters(TC_mod1_M, digits= 2, ci= 0.85) %>% 
  mutate(Component= "conditional",
        Effects= "fixed",
        Model= "Ov_coeff ~ p_distance + diet_dist+Lat_abs")%>% 
  select(-SE, -z, -df_error)
Code
TC_mods_tab <- rbind(TC_mods, TC_mods_F, TC_mods_C, TC_mods_M)

kbl(TC_mods_tab, 
    caption = "Temporal co-occurrence selected models", digits = 3) %>%
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = F) %>% 
    pack_rows("Temporal co-occurrence models -all data",1, nrow(TC_mods)) %>%
    pack_rows("Temporal co-occurrence models -Felidae as dominant competitor",1+ nrow(TC_mods),nrow(TC_mods)+ nrow(TC_mods_F)) %>%
  pack_rows("Temporal co-occurrence models -Canidae as dominant competitor",1+nrow(TC_mods)+ nrow(TC_mods_F), nrow(TC_mods)+ nrow(TC_mods_F)+ nrow(TC_mods_C)) %>% 
  pack_rows("Temporal co-occurrence models -Mustelidae as dominant competitor", 1+nrow(TC_mods)+ nrow(TC_mods_F)+ nrow(TC_mods_C), nrow(TC_mods)+ nrow(TC_mods_F)+ nrow(TC_mods_C)+ nrow(TC_mods_M))
Temporal co-occurrence selected models
Parameter Coefficient CI CI_low CI_high p Effects Component Model
Temporal co-occurrence models -all data
(Intercept) 0.681 0.85 0.607 0.754 0.000 fixed conditional Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)
Lat_abs 0.127 0.85 0.061 0.193 0.006 fixed conditional Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)
mass_ratio -0.067 0.85 -0.111 -0.024 0.025 fixed conditional Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)
p_distance -0.107 0.85 -0.155 -0.059 0.001 fixed conditional Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)
(Intercept) 1.939 0.85 1.863 2.015 0.000 fixed dispersion Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)
p_distance -0.276 0.85 -0.362 -0.191 0.000 fixed dispersion Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)
Samp_dur 0.015 0.85 -0.063 0.093 0.778 fixed dispersion Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)
Lat_abs 0.318 0.85 0.231 0.405 0.000 fixed dispersion Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)
SD (Intercept) 0.326 0.85 0.267 0.398 NA random conditional Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label)
(Intercept) 0.724 0.85 0.647 0.802 0.000 fixed conditional Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)
Lat_abs 0.123 0.85 0.056 0.189 0.008 fixed conditional Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)
I(mass_ratio^2) -0.038 0.85 -0.066 -0.009 0.054 fixed conditional Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)
p_distance -0.108 0.85 -0.156 -0.060 0.001 fixed conditional Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)
(Intercept) 1.938 0.85 1.862 2.014 0.000 fixed dispersion Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)
p_distance -0.287 0.85 -0.373 -0.201 0.000 fixed dispersion Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)
Samp_dur 0.022 0.85 -0.056 0.100 0.687 fixed dispersion Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)
Lat_abs 0.313 0.85 0.225 0.400 0.000 fixed dispersion Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)
SD (Intercept) 0.328 0.85 0.268 0.400 NA random conditional Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label)
(Intercept) 0.764 0.85 0.686 0.843 0.000 fixed conditional Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label)
I(mass_ratio^2) -0.060 0.85 -0.090 -0.031 0.004 fixed conditional Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label)
p_distance -0.146 0.85 -0.200 -0.091 0.000 fixed conditional Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label)
I(mass_ratio^2):p_distance 0.071 0.85 0.031 0.110 0.011 fixed conditional Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label)
(Intercept) 1.951 0.85 1.875 2.028 0.000 fixed dispersion Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label)
p_distance -0.299 0.85 -0.385 -0.212 0.000 fixed dispersion Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label)
Samp_dur 0.000 0.85 -0.078 0.079 0.993 fixed dispersion Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label)
Lat_abs 0.275 0.85 0.189 0.362 0.000 fixed dispersion Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label)
SD (Intercept) 0.356 0.85 0.295 0.429 NA random conditional Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label)
Temporal co-occurrence models -Felidae as dominant competitor
(Intercept) 0.586 0.85 0.366 0.805 0.000 fixed conditional Ov_coeff ~ p_distance*diet_dist+ (1|Label)
p_distance 0.267 0.85 -0.012 0.546 0.168 fixed conditional Ov_coeff ~ p_distance*diet_dist+ (1|Label)
diet_distSame_diet -0.074 0.85 -0.286 0.139 0.617 fixed conditional Ov_coeff ~ p_distance*diet_dist+ (1|Label)
p_distance:diet_distSame_diet -0.507 0.85 -0.797 -0.217 0.012 fixed conditional Ov_coeff ~ p_distance*diet_dist+ (1|Label)
(Intercept) 2.209 0.85 2.086 2.332 0.000 fixed dispersion Ov_coeff ~ p_distance*diet_dist+ (1|Label)
p_distance -0.337 0.85 -0.452 -0.222 0.000 fixed dispersion Ov_coeff ~ p_distance*diet_dist+ (1|Label)
Samp_dur 0.012 0.85 -0.083 0.107 0.860 fixed dispersion Ov_coeff ~ p_distance*diet_dist+ (1|Label)
Lat_abs 0.407 0.85 0.265 0.549 0.000 fixed dispersion Ov_coeff ~ p_distance*diet_dist+ (1|Label)
SD (Intercept) 0.430 0.85 0.347 0.534 NA random conditional Ov_coeff ~ p_distance*diet_dist+ (1|Label)
Temporal co-occurrence models -Canidae as dominant competitor
(Intercept) 0.370 0.85 0.173 0.567 0.007 fixed conditional Ov_coeff ~ Lat_abs+ mass_ratio+ (1|Label)
Lat_abs 0.377 0.85 0.225 0.529 0.000 fixed conditional Ov_coeff ~ Lat_abs+ mass_ratio+ (1|Label)
mass_ratio -0.407 0.85 -0.550 -0.264 0.000 fixed conditional Ov_coeff ~ Lat_abs+ mass_ratio+ (1|Label)
(Intercept) 1.869 0.85 1.608 2.131 0.000 fixed dispersion Ov_coeff ~ Lat_abs+ mass_ratio+ (1|Label)
Samp_dur 0.009 0.85 -0.191 0.209 0.948 fixed dispersion Ov_coeff ~ Lat_abs+ mass_ratio+ (1|Label)
Lat_abs 0.686 0.85 0.444 0.928 0.000 fixed dispersion Ov_coeff ~ Lat_abs+ mass_ratio+ (1|Label)
SD (Intercept) 0.371 0.85 0.252 0.548 NA random conditional Ov_coeff ~ Lat_abs+ mass_ratio+ (1|Label)
Temporal co-occurrence models -Mustelidae as dominant competitor
(Intercept) -0.051 0.85 -0.249 0.146 0.709 fixed conditional Ov_coeff ~ p_distance + diet_dist+Lat_abs
p_distance 0.392 0.85 0.242 0.543 0.000 fixed conditional Ov_coeff ~ p_distance + diet_dist+Lat_abs
diet_distSame_diet 0.718 0.85 0.481 0.954 0.000 fixed conditional Ov_coeff ~ p_distance + diet_dist+Lat_abs
Lat_abs 0.387 0.85 0.243 0.531 0.000 fixed conditional Ov_coeff ~ p_distance + diet_dist+Lat_abs

Goftest of temporal selected models

Code
TC_best_goft_list <- list(TC_mod1, TC_mod2, TC_mod3) 
TC_best_goft <- lapply(TC_best_goft_list, simulateResiduals, plot=T)

Ov_coeff ~ Lat_abs+ mass_ratio+ p_distance + (1|Label) goftest -all data

Ov_coeff ~ Lat_abs+ I(mass_ratio^2)+ p_distance+ (1|Label) goftest - -all data

Ov_coeff ~ I(mass_ratio^2)*p_distance+ (1|Label) goftest- -all data

Code
TC_best_goft_list_F <- list(TC_mod1_F) 
TC_best_goft_F <- lapply(TC_best_goft_list_F, simulateResiduals, plot=T)

Ov_coeff ~ p_distance*diet_dist+ (1|Label) goftest -Felidae as dominant competitor

Code
TC_best_goft_list_C <- list(TC_mod1_C) 
TC_best_goft_C <- lapply(TC_best_goft_list_C, simulateResiduals, plot=T)

Ov_coeff ~ mass_ratio + (1 | Label) goftest -Canidae as dominant competitor

Code
plot(TC_mod1_M)

Predictions

Code
# Spatial all data

SC_pred_mass <- ggemmeans(SC_mod1, 
                          terms = c("mass_ratio[-1.2:3.1 by=.2]"), 
                          ci_level=.85,
                          ci.lvl = .85) %>% 
  mutate(mass_real= (x* attr(scale(spatC_db$mass_ratio), "scaled:scale"))+ attr(scale(spatC_db$mass_ratio), "scaled:center"))

SC_pred_pdist <- ggemmeans(SC_mod1, 
                           terms = "p_distance[-2.3:1.2 by=.2]", 
                           ci_level=.85,
                          ci.lvl = .85) %>% 
  mutate(p_real= (x* attr(scale(spatC_db$p_distance), "scaled:scale"))+ attr(scale(spatC_db$p_distance), "scaled:center"))

# Spatial Felidae
SCp_distvec_F <- c(max(spatC_modsdf_F$p_distance), mean(spatC_modsdf_F$p_distance),
               min(spatC_modsdf_F$p_distance))

SCp_latvec_F <- c(max(spatC_modsdf_F$Lat_abs), mean(spatC_modsdf_F$Lat_abs),
               min(spatC_modsdf_F$Lat_abs))

SC_pred_massxp_F <- ggemmeans(SC_mod4_F, 
                              terms =c("mass_ratio[all]", "p_distance[SCp_distvec_F]"),
                              ci_level=.85,
                              ci.lvl = .85) %>% 
  mutate( mass_real= (x* attr(scale(spatC_db$mass_ratio), "scaled:scale"))+ attr(scale(spatC_db$mass_ratio), "scaled:center"),
        p_disreal= (as.numeric(as.character(group))* attr(scale(spatC_db$p_distance), "scaled:scale"))+ attr(scale(spatC_db$p_distance), "scaled:center")) %>% 
  mutate(across(p_disreal, round, 2))

SC_pred_massxl_F <- ggemmeans(SC_mod1_F, 
                              terms =c("mass_ratio[all]", "Lat_abs[SCp_latvec_F]"),
                              ci_level=.85,
                              ci.lvl = .85) %>% 
  mutate( mass_real= (x* attr(scale(spatC_db$mass_ratio), "scaled:scale"))+ attr(scale(spatC_db$mass_ratio), "scaled:center"),
        lat_real= (as.numeric(as.character(group))* attr(scale(spatC_db$Lat_abs), "scaled:scale"))+ attr(scale(spatC_db$Lat_abs), "scaled:center")) %>% 
  mutate(across(lat_real, round, 2))

# Temporal all
TCp_distvec <- c(max(tempC_modsdf$p_distance), mean(tempC_modsdf$p_distance),
               min(tempC_modsdf$p_distance))

TC_pred_massxp <- ggemmeans(TC_mod3, 
                            terms =c("mass_ratio[-1.3:3.1 by=.2]", 
                                              "p_distance[TCp_distvec]"),
                            ci_level=.85,
                            ci.lvl = .85) %>% 
  mutate( mass_real= (x* attr(scale(tempC_db$mass_ratio), "scaled:scale"))+ attr(scale(tempC_db$mass_ratio), "scaled:center"),
        p_disreal= (as.numeric(as.character(group))* attr(scale(tempC_db$p_distance), "scaled:scale"))+ attr(scale(tempC_db$p_distance), "scaled:center")) %>% 
  mutate(across(p_disreal, round, 2))

TC_pred_lat <- ggemmeans(TC_mod1, terms = c("Lat_abs[-1.6:2.3 by=.2]"),
                         ci_level=.85,
                         ci.lvl = .85) %>% 
  mutate(lat_real= (x* attr(scale(tempC_db$Lat_abs), "scaled:scale"))+ attr(scale(tempC_db$Lat_abs), "scaled:center"))

# Temporal Felidae

TC_pred_pxdiet_F1 <- ggemmeans(TC_mod1_F, 
                              terms = c("p_distance[-0.16:1.28 by=.2]", "diet_dist[Diff_diet]"),
                              ci_level=.85,
                              ci.lvl = .85) %>% 
  mutate(p_real= (x* attr(scale(tempC_db$p_distance), "scaled:scale"))+ attr(scale(tempC_db$p_distance), "scaled:center"))

TC_pred_pxdiet_F2 <- ggemmeans(TC_mod1_F, 
                              terms = c("p_distance[-2.3:1.08 by=.2]", "diet_dist[Same_diet]"),
                              ci_level=.85,
                              ci.lvl = .85) %>% 
  mutate(p_real= (x* attr(scale(tempC_db$p_distance), "scaled:scale"))+ attr(scale(tempC_db$p_distance), "scaled:center"))


TC_pred_pxdiet_F <- rbind(TC_pred_pxdiet_F1, TC_pred_pxdiet_F2)

# Temporal Canidae 

TC_pred_mass_C <- ggemmeans(TC_mod1_C, 
                            terms = c("mass_ratio[-1.2:1.28 by=.2]"),
                             ci_level=.85,
                             ci.lvl = .85) %>% 
  mutate(mass_real= (x* attr(scale(tempC_db$mass_ratio), "scaled:scale"))+ attr(scale(tempC_db$mass_ratio), "scaled:center"))

TC_pred_lats_C <- ggemmeans(TC_mod1_C, 
                            terms = c("Lat_abs[-1.4:2.3]"),
                            ci_level=.85,
                            ci.lvl = .85) %>% 
  mutate(lat_real= (x* attr(scale(tempC_db$Lat_abs), "scaled:scale"))+ attr(scale(tempC_db$Lat_abs), "scaled:center"))

# Temporal Mustelidae

TC_pred_pdist_M <- ggemmeans(TC_mod1_M, 
                             terms = c("p_distance[-1.7:1.3 by=.2]"),
                             ci_level=.85,
                             ci.lvl = .85)%>% 
  mutate(p_real= (x* attr(scale(tempC_db$p_distance), "scaled:scale"))+ attr(scale(tempC_db$p_distance), "scaled:center"))

TC_pred_diet_M <- ggemmeans(TC_mod1_M, terms = c("diet_dist"),
                            ci_level=.85,
                            ci.lvl = .85)

TC_pred_lat_M <- ggemmeans(TC_mod1_M, terms = c("Lat_abs[-1.4:2.3 by=.2]"))%>% 
  mutate(lat_real= (x* attr(scale(tempC_db$Lat_abs), "scaled:scale"))+ attr(scale(tempC_db$Lat_abs), "scaled:center"))


Lat_TC <- bind_rows(TC_pred_lat, TC_pred_lats_C, TC_pred_lat_M) %>% 
  mutate(data_from= c(rep("All species", length(TC_pred_lat$x)),
                      rep("Canidae", length(TC_pred_lats_C$x)),
                      rep("Mustelidae", length(TC_pred_lat_M$x))))

Plots

Code
# Spatial all data
(SC_mass_plot <- ggplot(SC_pred_mass)+
   geom_hline(yintercept = 1, linetype= "dashed", size= 1)+
   geom_ribbon(aes(x= mass_real, y= predicted,
                  ymin= conf.low, ymax= conf.high)
              , alpha=0.7, fill= "#fde725")+
  geom_line(aes(x= mass_real, y=predicted),
            size= 0.8 )+
  labs(x= "ln(Mass ratio)",
        y= "Spatial Overlap",
       tag= "A")+
  scale_x_continuous(expand = c(0,0))+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto")))

Code
(SC_pdist_plot <- ggplot(SC_pred_pdist)+
    geom_hline(yintercept = 1, linetype= "dashed", size= 1)+
    geom_ribbon(aes(x= p_real, y= predicted,
                  ymin= conf.low, ymax= conf.high)
              , alpha=0.7, fill= "#fde725")+
  geom_line(aes(x= p_real, y=predicted),
            size= 0.8 )+
  labs(x= "Phylogenetic distance",
        y= "Spatial Overlap",
       tag= "B")+
  scale_x_continuous(expand = c(0,0))+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto")))

Code
# Spatial Felidae

(SC_mxp_plot_F <- ggplot(SC_pred_massxp_F)+
    geom_hline(yintercept = 1, linetype= "dashed", size= 1)+
  geom_ribbon(aes(x= mass_real, y= predicted,
                  ymin= conf.low, ymax= conf.high,
                  fill= as.factor(p_disreal),
                  group= as.factor(p_disreal))
              , alpha= 0.7, linewidth= 1)+
    scale_fill_viridis_d()+
  geom_line(aes(x= mass_real, y=predicted, group= as.factor(p_disreal),
                linetype= as.factor(p_disreal)),
            size= 0.8 )+
  labs(x= "ln(Mass ratio)",
        y= "Spatial Overlap",
       group= "Phylogenetic \ndistance",
       linetype= "Phylogenetic \ndistance",
       fill= "Phylogenetic \ndistance",
       tag= "C")+
  scale_x_continuous(expand = c(0,0))+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto"),
         legend.direction="horizontal",
         legend.position = c(0.5, 0.10),
         legend.background = element_blank()))

Code
(SC_mxl_plot_F <- ggplot(SC_pred_massxl_F)+
    geom_hline(yintercept = 1, linetype= "dashed", size= 1)+
  geom_ribbon(aes(x= mass_real, y= predicted,
                  ymin= conf.low, ymax= conf.high,
                  fill= as.factor(lat_real),
                  group= as.factor(lat_real))
              , alpha= 0.7, linewidth= 1)+
    scale_fill_viridis_d()+
  geom_line(aes(x= mass_real, y=predicted, group= as.factor(lat_real),
                linetype= as.factor(lat_real)),
            size= 0.8 )+
  labs(x= "ln(Mass ratio)",
        y= "Spatial Overlap",
       group= "Absolute \nlatitude",
       linetype= "Absolute \nlatitude",
       fill= "Absolute \nlatitude",
       tag= "D")+
  scale_x_continuous(expand = c(0,0))+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto"),
         legend.direction="horizontal",
         legend.position = c(0.5, 0.10),
         legend.background = element_blank()))

Code
# Temporal all

(TC_mxp_plot <- ggplot(TC_pred_massxp)+
  geom_ribbon(aes(x= mass_real, y= predicted,
                  ymin= conf.low, ymax= conf.high,
                  fill= as.factor(p_disreal),
                  group= as.factor(p_disreal))
              , alpha= 0.7, linewidth= 1)+
    scale_fill_viridis_d()+
  geom_line(aes(x= mass_real, y=predicted, group= as.factor(p_disreal),
                linetype= as.factor(p_disreal)),
            size= 0.8 )+
  labs(x= "ln(Mass ratio)",
        y= "Temporal Overlap",
       group= "Phylogenetic \ndistance",
       fill= "Phylogenetic \ndistance",
       linetype= "Phylogenetic \ndistance",
       tag= "E")+
  scale_x_continuous(expand = c(0,0))+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto"),
         legend.direction="horizontal",
         legend.position = c(0.45, 0.10),
         legend.background = element_blank()))

Code
# TEmporal Felidae

(TC_pxd_plot_F <- ggplot(TC_pred_pxdiet_F)+
   geom_ribbon(aes(x= p_real, y= predicted,
                  ymin= conf.low, ymax= conf.high,
                  fill= group, 
                  group= group,
                  linetype= group)
              , alpha=0.7)+
    scale_fill_viridis_d()+
  geom_line(aes(x= p_real, y=predicted, group= group,
                linetype= group),
            size= 0.8 )+
  labs(x= "Phylogenetic distance",
        y= "Temporal Overlap",
       group= "Diet \ndistance",
       fill= "Diet \ndistance",
       linetype= "Diet \ndistance",
       tag= "F")+
  scale_x_continuous(expand = c(0,0))+
    scale_y_continuous(limits = c(0.3,1))+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto"),
         legend.direction="horizontal",
         legend.position = c(0.55, 0.10),
         legend.background = element_blank()))

Code
# Temporal Canidae

(TC_mass_plot_C <- ggplot(TC_pred_mass_C)+
    geom_ribbon(aes(x= mass_real, y= predicted,
                  ymin= conf.low, ymax= conf.high)
              , alpha=0.7, fill= "#fde725")+
  geom_line(aes(x= mass_real, y=predicted),
            size= 0.8 )+
  labs(x= "ln(Mass ratio)",
        y= "Temporal Overlap",
       tag= "G")+
  scale_x_continuous(expand = c(0,0))+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto")))

Code
# Temporal Mustelidae 

(TC_p_plot_M <- ggplot(TC_pred_pdist_M)+
  geom_ribbon(aes(x= p_real, y= predicted,
                  ymin= conf.low, ymax= conf.high)
              , alpha=0.7, fill= "#fde725")+
  geom_line(aes(x= p_real, y=predicted),
            size= 0.8 )+
  labs(x= "Phylogenetic distance",
        y= "Temporal Overlap",
       tag= "H")+
  scale_x_continuous(expand = c(0,0))+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto"))
  )

Code
(TC_diet_plot_M <- ggplot(TC_pred_diet_M)+
   geom_errorbar(aes(x= x, y= predicted,
                  ymin= conf.low, ymax= conf.high)
              , size= 1, width= 0.1)+
  geom_point(aes(x= x, y=predicted),
            size= 4)+
  labs(x= "Diet distance",
        y= "Temporal Overlap",
       tag= "I")+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto"))
  )

Code
(TC_Lat_plot <-  ggplot(Lat_TC)+
   geom_ribbon(aes(x= lat_real, y= predicted,
                  ymin= conf.low, ymax= conf.high,
                  group= data_from, fill=data_from)
              , alpha=0.7)+
  geom_line(aes(x= lat_real, y=predicted, linetype= data_from, group= data_from),
            size= 0.8)+
    scale_fill_viridis_d()+
  labs(x= "Absolute latitude",
        y= "Temporal Overlap",
       fill= "Dominant \ncompetitor",
       linetype= "Dominant \ncompetitor",
       tag= "J")+
   theme_bw()+
    scale_x_continuous(expand = c(0,0))+
  theme_bw()+
   theme(text = element_text(size=13, family = "Roboto"),
         legend.direction="vertical",
         legend.position = c(1.2, 0.5),
         legend.background = element_blank()))

Code
(CPrediction_plot <- (SC_mass_plot + SC_pdist_plot+ SC_mxp_plot_F + 
                       SC_mxl_plot_F+ TC_mxp_plot+ TC_pxd_plot_F+ 
                       TC_mass_plot_C+ TC_p_plot_M+ TC_diet_plot_M+
                       TC_Lat_plot)+
  plot_layout(ncol = 3))

Code
ggsave(filename = "Figs/Cpreds_plot.svg", plot = CPrediction_plot,
        width = 11.5, height = 11.5)

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